Research Interests.
I work in Probability theory and Stochastic analysis. My PhD thesis was on Harnack inequalities; I used a mixture of analysis and probability to arrive at the results. Since then, I am also interested in the analysis of PDEs.
While doing a postdoc at the University of Utah, I got interested in Stochastic partial differential equations. More specifically, I am interested in the long time behavior of solutions. Here is a list of publications.
Publications:
1. Title: Harmonic functions for a class of integro-differential operators.
Published: Potential Analysis, 31(2009), no. 1, 22--44, arxiv version.
2. Title: Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part. Published: Electronic Journal of probability, 14(2009), no. 11, 314--340. arxiv version
3. Title: A local time correspondence for stochastic partial differential equations.
Coauthors: Davar Khoshnevisan and Eulalia Nualart
Published: To appear in Transactions of A.M.S, arxiv version
4. Title: Intermittence and nonlinear parabolic stochastic partial differential equations.
Coauthors: Davar Khoshnevisan
Published: Electronic Journal of probability, 14(2009), no. 21, 548--568, arxiv version.
5. Title: An assymtotic theory for randomly-forced discrete nonlinear heat equation.
Coauthors: Davar Khoshnevisan
Published: submitted, arxiv version.
6. Title: On the global maximum of the solution to a stochastic heat equation with compactly-support initial data.
Coauthors: Davar Khoshnevisan
Published: To appear in Annales de L'institut Poincare, arxiv version
7. Title: Dynkin's isomorphism theorem and the stochastic heat equation.
Coauthors: Nathalie Eisenbaum and Davar Khoshnevisan
Published: To appear in Potential Analysis, arxiv version
8. Title: An inequality for a class of Markov processes.
Published: Submitted, arxiv version
9. Title: On Stochastic Heat Equation with Spatially-colored Random forcing
Coauthors: Davar Khoshnevisan
Published: Submitted, preprint version.
Comments: This is a monograph.