Existence and uniqueness of solutions to degenerate stochastic integro-differential equations are proved in Bessel potential spaces.
It\^o's formula for jump processes in $L_p$-spaces
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abstract
We present an It\^o formula for the $L_p$-norm of jump processes having stochastic differentials in $L_p$-spaces. The main results extend well-known theorems of Krylov to the case of processes with jumps, and which can be used to prove existence and uniqueness theorems in $L_p$-spaces for SPDEs driven by L\'evy processes.
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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.