Existence and uniqueness of solutions to degenerate stochastic integro-differential equations are proved in Bessel potential spaces.
On the Cauchy problem for stochastic integrodifferential parabolic equations in the scale of Lp-spaces of generalized smoothness
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abstract
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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math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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On $L_p$-Solvability of Stochastic Integro-Differential Equations
Existence and uniqueness of solutions to degenerate stochastic integro-differential equations are proved in Bessel potential spaces.