Summary: DOI: 10.1007/s00245-002-0755-1
Appl Math Optim 46:8996 (2002)
© 2002 Springer-Verlag New York Inc.
Stochastic Vorticity and Associated Filtering Theory
and Gopinath Kallianpur2
1Department of Statistics, University of Michigan,
Ann Arbor, MI 48109-1092, USA
2Department of Statistics, University of North Carolina,
Chapel Hill, NC 27599-3260, USA
Abstract. The focus of this work is on a two-dimensional stochastic vorticity
equation for an incompressible homogeneous viscous fluid. We consider a signed
measure-valued stochastic partial differential equation for a vorticity process based
on the SkorohodIto evolution of a system of N randomly moving point vortices. A
nonlinear filtering problem associated with the evolution of the vorticity is consid-
ered and a corresponding FujisakiKallianpurKunita stochastic differential equa-
tion for the optimal filter is derived.
Key Words. Nonlinear filtering, Stochastic vorticity, Systems of stochastic dif-
ferential equations, Signed measure-valued SPDE.
AMS Classification. 60G35, 60H20, 60H15.