Journal article
Existence and uniqueness of a mild solution to the stochastic heat equation with white and fractional noises
Year:
2018Published in:
American Mathematical SocietyFractional Brownian motion
stochastic partial differential equation
Green’s
function
We prove the existence and uniqueness of a mild solution for a class of nonautonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset D ⊂ Rd and involving standard and fractional L2(D)-valued Brownian motions. We assume that the coefficients are homogeneous, Lipschitz continuous, and the coefficient at the fractional Brownian motion is an affine function.