Rabi Bhattacharya
Office: Math 603
Phone: 520-626-5647
E-mail:
rabi@math.arizona.edu
Academic Career
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Ph.D.(Statistics), University of Chicago, 1967 |
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Assistant Professor of Statistics, University of California, Berkeley, 1967-72 |
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Associate professor of Mathematics, University of Arizona, 1972-77 |
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Professor of Mathematics, University of Arizona, 1977-82 |
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Professor of Mathematics: Indiana University,1982-2002 |
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Professor of Mathematics: University of Arizona,2002... |
Research Interests
1. Probability
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.
2. Statistics
Large sample theory; Edgeworth expansions and bootstrapping; statistics on shape spaces and other manifolds.
3 Applications of probability to Economics: growth under uncertainity
Recent Publications
Books:
1. Random Dynamical Systems (with M. Majumdar). Cambridge University Press. (2007).
2. A Basic Course in Probability Theory (with E. C. Waymire). Springer. (2007).
3. Theory and Applications of Stochastic Processes (with E.C.Waymire). Springer. (2009) Graduate Text in Mathematics. To appear.
Articles:
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.
Course Information