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arxiv: 1805.03232 · v1 · pith:55EPRJGVnew · submitted 2018-05-08 · 🧮 math.AP · math.PR

On the Cauchy problem for stochastic integrodifferential parabolic equations in the scale of Lp-spaces of generalized smoothness

R. Mikulevicius , C. Phonsom This is my paper
classification 🧮 math.AP math.PR
keywords levylp-spacesparabolicproblemstochasticassociatedcauchycondition
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Stochastic parabolic integro-differential problem is considered in the whole space. By verifying H\"ormander condition, the existence and uniqueness is proved in Lp-spaces of functions whose regularity is defined by a scalable Levy measure. Some rough probability density function estimates of the associated Levy process are used as well.

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  1. On $L_p$-Solvability of Stochastic Integro-Differential Equations

    math.AP 2019-07 unverdicted novelty 4.0

    Existence and uniqueness of solutions to degenerate stochastic integro-differential equations are proved in Bessel potential spaces.