On Classical Solutions of Linear Stochastic Integro-Differential Equations

James-Michael Leahy; Remigijus Mikulevicius

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arXiv · 1404.0345

On Classical Solutions of Linear Stochastic Integro-Differential Equations

James-Michael Leahy·Remigijus Mikulevicius

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Abstract

We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows associated with the equations. The equations are forward and the derivation of existence does not use the "general theory" of SPDEs. Uniqueness is proved in the class of classical solutions with polynomial growth.

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James-Michael Leahy, Remigijus Mikulevicius. 2014-11-26. On Classical Solutions of Linear Stochastic Integro-Differential Equations. https://arxiv.org/abs/1404.0345

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