RABI BHATTACHARYA the Department of Mathematics the University of Arizona 617 N Santa Rita Tucson, AZ 85721

RABI BHATTACHARYA The Department of Mathematics The University of Arizona 617 N Santa Rita Tucson, AZ 85721.

1. Degrees

Ph.D. (Statistics) University of Chicago, 1967.

2. Positions Held:

Regular Positions 1967-72 Assistant Professor of Statistics, Univ. of California, Berkeley. 1972-77 Associate Professor of Mathematics, University of Arizona. 1977-82 Professor, University of Arizona. 1982-02 Professor, Indiana University (Dept. of Mathematics). 2002- Professor of Mathematics and member of BIO5 faculty, University of Arizona.

Visiting Positions 1978-79 Visiting Professor, Indian Statistical Institute. 1979 (Summer) Distinguished Visiting Professor, Math. and Civil Engi- neering, University of Mississippi. 1992 Visiting Professor, University of Bielefeld, Germany, June 26-July 28. 1994 Visiting Professor, University of Bielefeld, Germany, Feb. 15-April 15. 1994 Visiting Professor, University of G¨ottingen, Germany, April 15-June 15. 1996 Visiting Professor, University of Bielefeld, Germany, June 8-July 9. 2000 Visiting Scholar, Stanford University, June-September. 2000-01 Visiting Scholar, Oregon State University.

1 3. Honors and Awards: 1977 Special Invited Paper, Annals of Probability 1978 IMS Fellow 1989 DMV Lecturer (by invitation of the German Mathematical Society) 1994-95 Humboldt Prize (Alexander von Humboldt Forschungspreis) 1996 IMS Special Invited Lecture, IMS Annual Meeting, Chicago (Medal- lion Lecture) 1999 Special Invited Paper, Annals of Applied Probability 2000 Guggenheim Fellowship

4. Professional Associations: Fellow of Institute of Mathematical Statistics American Mathematical Society

5. Research Interests: 1. Markov processes in discrete and continuous time and stochastic diﬀeren- tial equations, and their applications to equations of mathematical physics, science, engineering and economics. 2. Analytical theory and reﬁnements of central limit theorems. 3. Large sample theory of mathematical statistics, including Edgeworth expansions and the bootstrap. 4. Statistics on manifolds and shape spaces (with applications to engineering, biology and medicine). 5. Shape constrained nonparametric curve estimation and bioassay.

2 6. SERVICE: Editorial Work: 1976-79 Associate Editor, Annals of Probability 1979-81 Associate Editor, Annals of Probability 1984-88 Associate Editor, J. Statistical Planning and Inference 1985 Associate Editor, Econometric Theory 1986-88 Associate Editor, J. Multivariate Analysis 1988 Advisory Board, J. Multivariate Analysis 1989 Journal of Multivariate Analysis, Econometric Theory 1990 Econometric Theory, Journal of Multivariate Analysis 1991 Journal of Multivariate Analysis, Econometric Theory 1992 Econometric Theory, J. of Multivariate Analysis 1993 Econometric Theory 1994 Econometric Theory 1995 Econometric Theory 1996 Econometric Theory 1997 Econometric Theory 1998 Econometric Theory 1999 Econometric Theory 2000-02 Annals of Probability, Associate Editor 2000-2002 J. Statist. Planning and Inference, Coordinating Editor 2002-2008 Statistica Sinica, Associate Editor 2006-2009 Annals of Applied Probability, Associate Editor 2010-2012 Sankhya, Associate Editor

Other Professional Service: 1990 Midwestern Probability Symposium (Member, Organizing Commit- tee, 1990). CBMS Regional Conference Board (Panelist 1990-92). 1993 International Conference on Probability, Bloomington, Indiana (Mem- ber, Organizing Committee). 1997 Chair, Session on Topics in Stochastic Processes, Bernoulli Soc./ISI Meeting (Dec. 1997).

3 1998-2001 Elected Member of IMS Council. 2001 Organizer of a session at the IMS Western Regional Meeting Vancou- ver (June, 2001). 2002 Member, NSF panel and workshop: The Role of Probability in Sci- entiﬁc and Mathematical Research: A Workshop in Current and Emerging Research Opportunities (June, 2002). 2004, 2005 Member, NSF CMG panel. 2006 Member, NSF Probability Panel. 2012 Organizer of a Special Session at the AMS Regional Meeting on Dispersion in Heterogeneous and/or Random Environments (with Edward Waymire) (October 2012).

Service to the University: 2006- 2012 Member, Executive Committee of the Statistics GIDP. 2009-2011 Chairman, Ph.D. Qualifying Exams of the Statistics GIDP. 2009-2010 Member of Personnel Committee, Dept of Mathematics. 2004- Undergraduate advisor, Dept of Mathematics. 2011,2012 Member of the Peer Review Committee of the Mathematics De- partment.

7. RESEARCH GUIDANCE: Fourteen students have completed Ph.D.s.

8. RESEARCH GRANTS: Nearly continuous support came from the NSF (DMS) since 1975. From 1968 to 1972 research support came from the U.S. Army Research division. Nearly ten years of support came from the NSF division in Environmental Engineering. NIH grant, 2008-2011. NSF grants DMS 0806011 (2008-2011), DMS 1107053 (2011-2014) and NSF 1406872 (2015-2016).

4 9. PUBLICATIONS: BOOKS: Research Monographs: 1. Normal Approximation and Asymptotic Expansions, (with R. Ranga Rao) Wiley, New York (1976). Russian Edition (1982). Revised Reprint by Krieger, Florida (1986). 2. Asymptotic Statistics (with M. Denker), Birkhauser, DMV Lecture Se- ries (May, 1990). 3. Random Dynamical Systems: Theory and Applications (with M. Ma- jumdar). Cambridge Univ. Press. (2007) 4. Normal Approximation and Asymptotic Expansions (2010). SIAM. Clas- sics in Applied Mathematics, No.64. (with Rao, R.Ranga). 5. Nonparametric Inference on Manifolds with Applications to Shape Spaces (2012). IMS/Cambridge Univ. Monograph Series # 2 (with A. Bhat- tacharya).

Graduate Texts: 1. SIAM Classics in Applied Mathematics 61 (SIAM reprint with Errata). Original edition published in 1990 by John Wiley, New York. 2. A Basic Course in Probability Theory (with E. Waymire). Springer. (2007). 3. Stochastic Processes With Applications (2009). SIAM. Classics in Ap- plied Mathematics, No.61. (with Waymire, Edward C). 4. A Course in Mathematical Statistics and Large Sample Theory (2016) (With L.Lin and V.Patrangenaru). Springer Series in Statistics.To appear.

ARTICLES:

1968 1. Berry-Esseen bounds for the multidimensional central limit theorem, Bull. Amer. Math. Soc., 74, 285-287.

1970

5 2. Rates of weak convergence for multidimensional central limit theorems, Theor. Probab. Appl., 15, 68-86.

1971 3. Rates of weak convergence and asymptotic expansions in classical central limit theorems, Ann. Math.Statist., 42, 241-259.

1972 4. Speed of convergence of the n-fold convolution of a probability measure on a compact group, Z. Wahrscheinlichkeitstheorie Ver. Geb., 25, 1-10. 5. Recent results on reﬁnements of the central limit theorem, Proc. Sixth Berkeley Symposium on Math. Stat. and Prob., 2, 453-484.

1973 6. Errors of normal approximation, Proc. International Conf. on Prob. Theory and Math. Statist., Vilnius, U.S.S.R., 117-119. 7. Random exchange economies, J. Econ. Theor, 6, 37-67 (with M. Ma- jumdar).

1975 8. On errors of normal approximation, Ann. Probab., 3, 815-828.

1976 9. On the stochastic foundations of the theory of water ﬂow through unsat- urated soil, Water Res. Research, 12, 503-512 (joint with V.K. Gupta and G. Sposito).

1977 10. Reﬁnements of the multidimensional central limit theorem and applications, Ann. Probab., 7, 1-28. (Special invited paper).

1978 11. On the validity of the formal Edgeworth expansion, Ann. Statist., 6,

6 434-451 (joint with J.K. Ghosh). 12. Criteria for recurrence and existence of invariant measures for multidimensional diﬀusions, Ann. Probab., 6, 541-553.

1979 13. On a statistical theory of solute transport in porous media, SIAM J. Appl. Math., 34, 485- 498 (joint with V.K. Gupta). 14. Foundational theories of solute transport in porous media: a critical review, Advances in Water Res., 2, 59-68 (joint with V.K. Gupta and G. Sposito).

1980 15. On global stability of some stochastic economic processes: A synthesis. Quantitative Economics and Development (Ed. by L.R. Klein, M. Nerlove and R.C. Tsiang), 19-43, Academic Press, New York (with M. Majumdar).

1981 16. A molecular approach to the foundations of solute transport in porous media, I. Conservative solutes inhomogeneous, saturated media, J. Hydrol- ogy, 50, 355-370 (joint with V.K. Gupta and G. Sposito). 17. Asymptotic behavior of several dimensional difusions, Nonlinear Stochas- tic Systems in Physics, Chemistry and Biology, (Ed. by L. Arnold and R. Lefever), Springer-Verlag.

1982 18. Recurrence and ergodicity of diﬀusions, (with S. Ramasubramanian) J. Mult. Analysis, 12, 95-122. 19. On classical limit theorems for diﬀusions, Sankhya 44, Ser. A, 47-71. 20. On the functional central limit theorem and the law of the iterated logarithm for Markov processes, Zeit. Wahr. Ver. Geb. 60, 185-201.

1983 21. The Hurst eﬀect under trend, (with V.K. Gupta and E. Waymire) J.

7 App. Prob. 20, 649-662. 22. A new derivation of the Taylor-Aris theory of solute dispersion in a capillary, (with V.K. Gupta) Water Res. Research, 19(4), 945-951. 23. A theoretical explanation of solute dispersion in saturated porous media at the Darcy scale, Water Res. Research, 19(4), 938-944 (joint with V.K. Gupta). 24. On the order of magnitude of cumulants of von Mises functionals and related statistics, Ann. Prob., 11(2), 346-354 (joint with M.L. Puri). 25. Fokker Planck equations, Encyclopedia of Statistical Sciences, Vol. 3 (ed. by S. Kotz and R. Johnson) Wiley, New York, (joint with C.M. New- man).

1984 26. Stochastic models in mathematical economics: A review, Statistics: Applications and New Directions, Proc. ISI Golden Jubilee Int. Conf. (ed. by J.K. Ghosh and G. Kalianpur), 55-99 (joint with M. Majumdar). 27. On the Taylor-Arts theory of solute transport in a capillary, SIAM J. Appl. Math. 44(l) (joint with V.K.Gupta).

1985 28. Some recent results on Cramer-Edgeworth expansions with applications, Multivariate Analysis VI: Proceedings of the Sixth International Sympo- sium on Multivariate Analysis, (P.R. Krishnaiah, ed.), 57-75. 29. Asymptotic expansions and applications, Proc. Fourth Vilnius Conf. on Prob. and Math. Stat., Vilnius, USSR. 30. A central limit theorem for diﬀusions with periodic coeﬃcients, Ann. Probab. 13, 385-396.

1986 31. Solute dispersion in multidimensional periodic porous media, Water Res. Research, 22(2), 156-164 (joint with V.K. Gupta).

1987

8 32. Some aspects of Edgeworth expansions in statistics and probability, New Perspectives in Theoretical and Applied Statistics (ed. by M. Puri, J. Villaplana and W. Wertz), Wiley, New York, 157-170.

1988 33. Central limit theorems for diffusions with almost periodic coefficients, Sankhya 50, 9-25 (joint with S.Ramasubramanian). 34. Asymptotics of a class of Markov processes which are not in general irreducible, Ann. Probab. 16, 1333-1347 (with O. Lee). 35. On moment conditions for valid formal Edgeworth expansions, J. Mult. Analysis 27, 68-79 (with J.K.Ghosh). 36. Ergodicity and the central limit theorem for a class of Markov Pro- cesses, J. Mult. Analysis 27, 80-90 (with O. Lee). 37. Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans, American Mineralogist, 73, 901-909 (with J. Ganguly and S. Chakraborty).

1989 38. Asymptotics of solute dispersion in periodic porous media, SIAM J. Appl. Math., 49, 86-98 (with V.K. Gupta and H.F. Walker). 39. Second order and Lpcomparisons between the bootstrap and empirical Edgeworth expansion methodologies, Ann. Statist., 17, 160-169 (with M. Qumsiyeh). 40. Controlled semi-Markov models-the discounted case, J. Stat. Plan. Inf., 21, 365-381 (with M.Majumdar). 41. Controlled semi-Markov models under long-run average rewards, J. Stat. Plan. Inf. 22, 223-242 (with M. Majumdar).

1990 42. Applications of central limit theorems to solute dispersion in saturated porous media: from kinetic to ﬁeld scales (with V.K. Gupta), in Dynamics of Fluids in Hierarchical Porous Media (Ed. by J. Cushman), Academic Press, 61-96.

9 1991 43. An extension of the classical method of images for the construction of reﬂecting diﬀusions (with E.C. Waymire), Proc. R.C. Bose Symp. on Prob., Math. Stat. and Design of Experiments, 155-164. Wiley (Eastern).

1992 44. Stability in distribution for a class of singular diﬀusions (with G. Basak). Ann. Probab., 20, 312-321. 45. Central limit theorems for diﬀusions: recent results, open problems and some applications (with S. Sen). Proc. I.I.M. Conf., Oxford Univ. Press. 46. A class of U-statistics and asymptotic normality of the number of k- clusters (with J.K. Ghosh). J. Multivariate Analysis 43, 300-330.

1993 47. The range of the inﬁnitesimal generator of an ergodic diﬀusion (with G. Basak), in Statistics and Probability: A Raghu Raj Bahadur Festschrift (J.K. Ghosh. et al, editors), 73- 81. Wiley. 48. Random iterations of two quadratic maps (with B.V. Rao) in Stochas- tic Processes: A Festschrift for G. Kallianpur (S. Cambanis et al., editors), 13-22. Springer-Verlag. 49. Markov processes: asymptotic stability in distribution, central limit theorems, In: Probability and Statistics (S.K. Basu, B.K. Sinha, editors), Narosa Publishing House, New Delhi, 33-43.

1994 50. Proxy and instrumental variable methods in regression with one regres- sor missing. J. Mult. Analysis 47, 123-138 (joint with D.K. Bhattacharyya).

1995 51. Ergodicity of ﬁrst order nonlinear autoregressive models, J. Theor. Probab. 8, 207219, (with C. Lee). 52. On geometric ergodicity of nonlinear autoregressive models, Statistics

10 and Probability Letters, 311-315 (with C. Lee). 53. Methodology and applications. In: Advances in Econometrics and Quantitative Economics, 88-122. (G.S. Maddala and P.C.B. Phillips, eds.), Blackwell, Oxford, U.K. (with M.L. Puri). 54. Time scales for Gaussian approximation and its breakdown under a hierarchy of periodic spatial heterogeneities, Bernoulli 1, 81-123 (with F. Goetze).

1996 55. Comparisons of Chisquare, Edgeworth expansions and bootstrap ap- proximations to the distributions of the frequency Chisquare, Sankhya, Ser. A 58, 57-68 (with N.H. Chan). 56. Asymptotics of iteration of i.i.d. symmetric stable processes, Re- search Developments in Probability and StatisticsMadan Puri Festschrift, (E. Brunner and M. Denker, eds.), 3-10 (with B.V. Rao).

1997 57. A hierarchy of Gaussian and non-Gaussian asymptotics of a class of Fokker-Planck equations with multiple scales, Nonlinear Analysis, Theory, Methods and Applications, 30, No. 1, 257-263, Proc. 2nd World Congress of Nonlinear Analysis, Athens, Greece, Elsevier Science Ltd. 58. Central limit theorems for diﬀusions: recent results, open problems and some applications, Probability and Its Applications (M.C. Bhattacharjee and S.K. Basu, eds.), 16-31, Oxford Univ. Press (with S. Sen). 59. Phase changes with time for a class of diﬀusions with multiple periodic spatial scales, and applications, Proc. 51st Session of the International Sta- tistical Institute, Istanbul, Turkey.

1999 60. Convergence to equilibrium of random dynamical systems generated by i.i.d. monotone maps with applications to economics. In: Asymptotics, Nonparametrics, and Time Series: Festschrift for M.L. Puri (S. Ghosh, Ed- itor), 713-742, Marcel Dekker (New York) (with M. Majumdar).

11 61. Speed of convergence to equilibrium and normality for diffusions with multiple periodic scales, Stochastic Processes and Applications, 80, 55-86 (with M. Denker and A. Goswami). 62. Multiscale diffusion processes with periodic coefficients and an applica- tion to solute transport in porous media. (Special Invited Paper), Annals of Applied Probability, 9, 951- 1020. 63. On a theorem of Dubins and Freedman. J. Theoretical Probab. 12, 1165-1185. (with M. Majumdar).

2000 64. Estimating the probability mass of unobserved support in random sam- pling. J. Statist Plan and Inf., 91-106 (with A. Almudevar and C.C. Sastri). 65. Random iteration of i.i.d. quadratic maps. In: Stochastics in Finite and Inﬁnite Dimensions: In Honor of G. Kallianpur (T. Hida, R.L. Karandikar, H. Kunita, B.S. Rajput, S. Watanabe and J. Xiang, eds.), Birkhauser, 49-58 (with K.B. Athreya). 66. Stochastic equivalence of convex ordered distributions and applications. Probability in Engineering and Informational Science, vol. 14, 33-48 (with M.C. Bhattacharjee). 67. A class of random continued fractions with singular equilibria. In: Per- spectives in Statistical Sciences (A.K. Basu, J.K. Ghosh, P.K. Sen and B.K. Sinha, eds.), Oxford University Press, 75-86 (with A. Goswami).

2001 68. On characterizing the probability of survival in a large competitive economy. Review of Economic Design, 6, 133-153 (with M. Majumdar). 69. On a class of stable random dynamical systems: Theory and applications. J. Economic Theory, 96, 208-229 (with M. Majumdar). 70. A note on the distribution of integrals of geometric Brownian mo- tion. Stat. and Probab. Letters, 55, 187-192 (with E. Thomann and E.C. Waymire). 71. Iterated random maps and some classes of Markov processes. In: Hand- book of Statistics, Vol. 19, (D.N. Shanbhag and C.R. Rao, eds.), Elsevier

12 Science. 145-170 (with E.C. Waymire).

2002 72. Markov processes and their applications. In Handbook of Stochastic Analysis and Applications (D. Kannan and V. Lakshmikantam, eds.). Mar- cel Dekker. 1-46. 73. An approach to the existence of unique invariant probabilities for Markov processes. In Limit Theorems in Probability and Statistics I (I.Berkes, E. Csaki, M. Csorgo, eds.) Budapest. 181-200. (with E. C. Waymire). 74.Phase changes with time for a class of autonomous multiscale diﬀusions. Sankhya, Ser. A. 64 741-762. (Special Issue in memory of D. Basu).

2003 75. Large sample theory of intrinsic and extrinsic sample means on manifolds- I. Ann. Statist. 31 1-29. (with V. Patrangenaru). 76. Majorizing Kernels and stochastic cascades with applications to in- compressible Navier-Stokes equations. Trans. Amer. Math. Soc. 355 5003-5040. (with L.Chen, S. Dobson, R.B. Guenther, C. Orum, M. Ossian- der, E. Thomann and E.C. Waymire).

2004 77. Random dynamical systems: a review. Econ. Theory. 23 13-38. (with M.Majumdar). 78. Stability in distribution of randomly perturbed quadratic maps as Markov processes. Ann. Appl. Probab. 14 1802-1809 (with M. Majumdar).

2005 79. Large sample theory of intrinsic and extrinsic sample means on manifolds- II. Ann. Statist. 1225-1259 (with V. Patrangenaru).

80. Semi-Markov Cascade Representations of Local Solutions to 3-D In- compressible Navier-Stokes equations (with L.Chen, S.Dobson, R.Guenther, C.Orum, M.Ossiander, E. Thomann, E.Waymire).(2005) In Probability and

13 Partial Diﬀerential Equations in Modern Applied Mathematics, IMA vol.140 Springer, 27-40

81. Phase changes with time and multiscale homogenizations of a class anomalous diﬀusions (2005). In Probability and partial diﬀerential equations in Modern Applied Mathematics. IMA Vol. 140. Springer, 11-26

2007 82. Consistency and asymptotic normality of the estimated eﬀective doses in bioassay. J. Statist. Plan. Inf. vol.137, 643-658 (with M. Kong).

2008 83. Nonparametric statistics on manifolds with applications to shape spaces. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, 282–301, Inst. Math. Stat. Collect., 3, Inst. Math. Statist., Beachwood, OH, 2008 (with Bhattacharya, Abhishek).

84. Statistics on Riemannian manifolds: asymptotic distribution and curvature. Proc. Amer. Math. Soc. 136 (2008), no. 8, 2959–2967 (with Bhattacharya, Abhishek).

2009 85. Statistics on manifolds with applications to shape spaces. Perspectives in mathematical sciences. I, 41–70, Stat. Sci. Interdiscip. Res., 7, World Sci. Publ., Hackensack, NJ, 2009, (with Bhattacharya, Abhishek).

86. Nonparametric inference for extrinsic means on size-and-(reﬂection)- shape manifolds with applications in medical imaging. J. Multivariate Anal. 100 (2009), no. 9, 1867–1882, (with Bandulasiri, Ananda. and Patrange- naru, Vic).

2010

14 87. An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies. Statistics & Probability Letters 80 (2010), 1947-1953. (with Lin, Lizhen).

88. Comment: ”Intrinsic shape analysis: geodesic PCA for Riemannian manifolds modulo isometric Lie group actions”. Statist. Sinica 20 (2010), no. 1, 58–63.

89. Random iterates of monotone maps. Rev. Econ. Des. 14 (2010), no. 1-2, 185–192 (with Majumdar, Mukul).

90. Limit theorems for monotone markov processes. Sankhya (2010). Volume 72-A, Part I. pp. 1-22. (with Majumdar, Mukul. and Hashimzade, Nigar).

2011

91. Nonparametric benchmark analysis in risk assessment: a compara- tive study by simulation and data analysis. Sankhya, Ser.B (2011). Volume 73 Issue 1, 144-163. (with Lin, Lizhen).

2012

92. On the speed of convergence of multidimensional diﬀusions to equilibrium (2012). Stoch. Dyn. 12, no. 1, 1150003-19 (with Wasielak, Aramian).

93. Nonparametric estimation of benchmark doses in environmental risk assessment (2012). Environmetrics 23, 717–728 (with Piegorsch, W.W., Xiong, H., and Lin, L.).

94. Extrinsic analysis on manifolds is computationally faster than intrinsic analysis with applications to quality control by machine vision. Applied Stochastic Models in Business and Industry (2012). Volume 28, Issue 3,

15 pages 222–235 (with Crane, M., , Ellingson, L., liu, X. , Patrangenaru, V.).

2013

95. Extrinsic data analysis on sample spaces with a manifold stratiﬁca- tion. Proceedings of the Seventh Congress of Romanian Mathematicians. Advances in mathematics, 241251, Ed. Acad. Roane, Bucharest, 2013. ( Buibas, M., Dryden, I. L., Ellingson,L. A., Groisser, D., Hendriks, H., Huckemann, S., Le,Huiling, Liu, X., Marron, J. S. , Osborne, D. E., Pa- trangenaru, V., Schwartzman, A., Thompson, H. W., Wood, A.T.A. ).

96. A nonparametric theory of statistics on manifolds. Limit theorems in probability, statistics and number theory, 173205, Springer Proc. Math. Stat., 42, Springer, Heidelberg, 2013.

97. Problems of ruin and survival in economics: Applications of limit theorems in probability.(Invited paper) Sankhya, The Indian Journal of Statistics. Ser.B, (2013), volume 75(2), 145–180. (with Majumdar, Mukul and Lin, Lizhen).

98. Recent progress in the nonparametric estimation of monotone curves -with applications to bioassay and environmental risk assessment. Compu- tational Statistics and Data Analysis (2013), volume 63, 63–80.

2014

99. Statistics on manifolds and landmarks based image analysis: a nonparametric theory with applications (with Discussions). J. Statist. Plann. Inference 145 (2014), 1-22. (with Patrangenaru, Vic).

100. Benchmark Dose Analysis via Nonparametric Regression Modeling. Risk Analysis, Vol. 34 (1) (2014), 135-151. (with Piegorsch, W., Xiong, H. and Lin, L.).

16 2015

101. Nonparametric benchmark dose estimation with continuous dose- response data. Scandinavian Journal of Statistics 42 (2015), 713–731 (with Lin, L and Piegorsch, W).

102. Sustainability in the Stochastic Ramsey Model. Journal of quantitative economics: journal of the Indian Econometric Society (2015), 13(2), 169-184. (with Kim, H. and Majumdar, M.)

103. Ruin probabilities in models of resource management and insurance: A synthesis. International Journal of Economic Theory (2015), 11(1), 59- 74. (with Majumdar, M.).

2016

104. Omnibus CLTs for Fr´echet means and nonparametric inference on non-Euclidean spaces. Proceedings of the American Mathematical Society (2016). To appear. Arxiv:1306.5806. (with Lin, L).