Title

Differential and stochastic equations in abstract Wiener space

Document Type

Article

Publication Date

1-1-1973

Abstract

This paper studies the differential equation ( ∂ ∂t) u(t, x) = 1 2trace A(t, x) D2u(t, x) A*(t, x) + 〈σ(t, x), Du(t, x)〉 - V(x) u(t, x), u(0, x) = φ(x) in infinite dimensional space. A Kac's type representation of solution in terms of function space integral is proved. Kac's method is modified to work nicely regardless of the dimensionality. © 1973.

Publication Source (Journal or Book title)

Journal of Functional Analysis

First Page

246

Last Page

256

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