Department of Statistics University of Michigan Ann Arbor, MI 48109
Phone: (734) 763-3499
Fax: (734) 763-4676
Degrees:
M.A., Mathematics, Lomonosov's Moscow State University
Ph.D., Statistics, University of North Carolina at Chapel Hill
Thesis at Mech-Mat: "Some geometric modifications of Stein's effect"
Ph.D. dissertation: "Topics in stochastic fluid dynamics"
Research interests:
Stochastic analysis, stochastic partial differential equations, particle systems
Applications to nonlinear filtering, hydrodynamics, stochastic finance
Gaussian random fields
Nonstationary time series
Nonparametric statistics
Selected papers and preprints:
"Stochastic vorticity and associated filtering theory" (pdf) (2002)
in Applied Mathematics & Optimization
"Nonlinear filtering with fractional Brownian motion" (pdf) (2002)
in Applied Mathematics & Optimization
"Fluid dynamics and stochastic evolution equations" (monograph)
"Large deviation principle for a stochastic Navier-Stokes
equation in its vorticity form for a two-dimensional incompressible flow"
(with Jie Xiong) (pdf) (2006)
in Discrete and Continuous Dynamical Systems, Series B
"Shrinkage estimation for convex polyhedral cones" (with Michael
Woodroofe) (pdf) (2004)
in Statistics & Probability Letters
"Product formula and independence criterion for multiple
Huang-Cambanis integrals" (with Sebastien Chivoret)
(pdf) (2006)
in Statistics & Probability Letters
"New method for optimal nonlinear filtering of noisy
observations by multiple stochastic fractional integral
expansions" (with Sebastien Chivoret)
(pdf) (2006)
in Computers & Mathematics with Applications
"Interaction between stock indices via changepoint analysis"
(with Martin Lenardon) (pdf) (2006)
in Applied Stochastic
Models in Business and Industry .
"Vortex theory approach to stochastic hydrodynamics" (pdf) (2007)
in Mathematical and
Computer Modelling .
"Stochastic transfer principle for multiple integrals with respect to
Gaussian random fields with applications" (pdf) (2007)
to appear in Integration: Mathematical Theory and Applications .
"On a class of stochastic differential equations driven by multiple
stochastic integrals".
"Stochastic Feynman integral: generalizations and properties".
"Inference for a class of SDEs driven by Volterra processes"
(with Bobby Reiner).
"Stochastic evolution equations for nonlinear filtering of random fields in the presence of fractional
Brownian sheet observation noise'' (with Matthew Linn) (pdf) (2008)
in Computers & Mathematics with Applications
"Representations of the optimal filter in the context of nonlinear filtering of random fields'' (with Matthew Linn) (2008)
accepted for publication in Stochastic Processes and their Applications
''Inverse stochastic transfer principle'' (with Matthew Linn) (2008)
Current federal grants:
Research is supported in part by NSF (DMS-0807635, PI) and
NSA (MDA904-07-1-0056, PI)
Ph.D. students:
Sebastien Chivoret
, Ph.D. 2005
Matthew Linn, current, expected graduation in 2009
Katarina Bodova, current, expected graduation in 2009
Robert C. Reiner Jr., current, expected graduation in 2010
