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Differential and stochastic equations in abstract Wiener space
Authors:Hui-Hsiung Kuo
Affiliation:Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903 U.S.A.
Abstract:
This paper studies the differential equation (??t) u(t, x) = 12trace A(t, x) D2u(t, x) A1(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.
Keywords:
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