Differential and stochastic equations in abstract Wiener space
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
Kuo, H. (1973). Differential and stochastic equations in abstract Wiener space. Journal of Functional Analysis, 12 (3), 246-256. https://doi.org/10.1016/0022-1236(73)90078-5