TY - JOUR
T1 - Stochastic calculus of variations for stochastic partial differential equations
AU - Ocone, Daniel
N1 - Funding Information:
* Supported in part by the NSF under Grant MCS-8301880.
PY - 1988/8
Y1 - 1988/8
N2 - This paper develops the stochastic calculus of variations for Hilbert space-valued solutions to stochastic evolution equations whose operators satisfy a coercivity condition. An application is made to the solutions of a class of stochastic pde's which includes the Zakai equation of nonlinear filtering. In particular, a Lie algebraic criterion is presented that implies that all finite-dimensional projections of the solution define random variables which admit a density. This criterion generalizes hypoellipticity-type conditions for existence and regularity of densities for finite-dimensional stochastic differential equations.
AB - This paper develops the stochastic calculus of variations for Hilbert space-valued solutions to stochastic evolution equations whose operators satisfy a coercivity condition. An application is made to the solutions of a class of stochastic pde's which includes the Zakai equation of nonlinear filtering. In particular, a Lie algebraic criterion is presented that implies that all finite-dimensional projections of the solution define random variables which admit a density. This criterion generalizes hypoellipticity-type conditions for existence and regularity of densities for finite-dimensional stochastic differential equations.
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U2 - 10.1016/0022-1236(88)90015-8
DO - 10.1016/0022-1236(88)90015-8
M3 - Article
AN - SCOPUS:38249028101
SN - 0022-1236
VL - 79
SP - 288
EP - 331
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -