Department of Mathematics
University of Arizona
Office: Math 603
|Ph.D.(Statistics), University of Chicago, 1967|
|Assistant Professor of Statistics, University of California, Berkeley, 1967-72|
|Associate professor of Mathematics, University of Arizona, 1972-77|
|Professor of Mathematics, University of Arizona, 1977-82|
|Professor of Mathematics: Indiana University,1982-2002|
|Professor of Mathematics: University of Arizona,2002...|
Asymptotic behavior of Markov processes; stochastic differential equations; central limit theorems and multiscale homogenization of linear second order PDEs; probablistic approach to certain classes of nonlinear PDEs such as the incompressible Navier-Stokes equations.
Large sample theory; Edgeworth expansions and bootstrapping; Statistics on shape spaces and other manifolds; Shape constrained nonparametric curve estimation and Bioassay.
3 Applications of probability to Economics: growth under uncertainity.
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 Series (May, 1990).
3. Random Dynamical Systems (with M. Majumdar). Cambridge University Press. (2007).
4. A Basic Course in Probability Theory (with E. C. Waymire). Springer. (2007).
5. Stochastic Processes With Applications (with E. C. Waymire). SIAM. Classics in Applied Mathematics, No.61. (2009)
6. Normal Approximation and Asymptotic Expansions (with R. Ranga Rao). SIAM. Classics in Applied Mathematics, No.64. (2010)
7. Nonparametric Inference on Manifolds with Applications to Shape Spaces (with A. Bhattacharya). IMS/Cambridge Univ. Monograph Series # 2 (2012).
1. Majoring kernels and stochastic cascades with applications to incompressible Navier-Stokes equations (with L.Chen, S.Dobson, R.Guenther, C.Orum, M.Ossiander, E. Thomann, E.Waymire). (2003) Trans. Amer. Math. Soc. 355, 5003-5040.
2. Semi-Markov Cascade Representations of Local Solutions to 3-D Incompressible Navier-Stokes equations (with L.Chen, S.Dobson, R.Guenther, C.Orum, M.Ossiander, E. Thomann, E.Waymire).(2005) In Probability and Partial Differential Equations in Modern Applied Mathematics, IMA vol.140 Springer, 27-40
3. Stability in distribution of randomly perturbed quadratic maps as Markov processes. (with M. Majumdar). (2004) Ann. Appl. Probab. 14, 1802-1809
4. Random dynamical systems: a review. (with M. Majumdar). (2004) Economic Theory, 23, 13-38.
5. 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
6. Large sample theory of intrinsic and extrinsic sample means on manifolds-I (with V.Ptrangenaru). (2003) Ann. Statist. 31, 1-29
7. Large sample theory of intrinsic and extrinsic sample means on maifolds-II (with V.Ptrangenaru). (2005) Ann Statist., 1225-1259
8. Consistency and asymptotic normality of the estimated effective doses in bioassay. (with M. Kong) (2006). J.Stat.Plan. Inf. 643-658
9. Statistics on Manifolds with Applications to Shape Spaces. (with Abhishek Bhattacharya) (2008). In Perspectives in Mathematical Sciences. Indian Statistical Institute, Bangalore. In Press.
9. Statistics on Riemannian Manifolds: Asymptotic Distribution and Curvature (with Abhishek Bhattacharya) (2008). Proceedings of the American Mathematical Society 136, 2957-2967.
10. Nonparametric Statistics on Manifolds with Applications to Shape Spaces (with Abhishek Bhattacharya) (2008). In Pushing the Limits of Contemporary Statistics: Contributions in honor of J.K. Ghosh. IMS Collections 3, 282-301.
11. Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging (with Bandulasiri, Ananda. and Patrangenaru, Vic) (2009). J. Multivariate Anal. 100 , no. 9, 1867--1882, .
12. An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies (with Lin, Lizhen) (2010). Statistics and Probability Letters 80, 1947-1953.
13. Comment: "Intrinsic shape analysis: geodesic PCA for Riemannian manifolds modulo isometric Lie group actions'' (2010). Statist. Sinica 20, no. 1, 58--63.
14. Random iterates of monotone maps (with Majumdar, Mukul) (2010). Rev. Econ. Des. 14, no. 1-2, 185--192.
15. Limit theorems for monotone markov processes (with Majumdar, Mukul. and Hashimzade, Nigar) (2010). Sankhya Volume 72-A, Part I. pp. 1-22.
16. Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis (with Lin, Lizhen) (2011). Sankhya, Ser.B. Volume 73 Issue 1, 144-163.
17. On the speed of convergence of multidimensional diffusions to equilibrium (with Wasielak, Aramian) (2012). Stoch. Dyn. 12, no. 1, 1150003-19.
18. Problems of ruin and survival in economics: Applications of limit theorems in probability (with Majumdar, Mukul and Lin, Lizhen) (2012). Sankhya, The Indian Journal of Statistics. Ser.B, . To appear.
Math 567B Fall 2012