On Classical Solutions of Linear Stochastic Integro-Differential Equations

摘要

We prove the existence of classical solutions to parabolic linear stochasticintegro-differential equations with adapted coefficients using Feynman-Kactransformations, conditioning, and the interlacing of space-inverses ofstochastic flows associated with the equations. The equations are forward andthe derivation of existence does not use the "general theory" of SPDEs.Uniqueness is proved in the class of classical solutions with polynomialgrowth.