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arxiv: 1904.12898 · v1 · pith:4V6NBKREnew · submitted 2019-04-29 · 🧮 math.PR

It\^o's formula for jump processes in L_p-spaces

Istv\'an Gy\"ongy , Sizhou Wu This is my paper
classification 🧮 math.PR
keywords processesspacesformulajumptheoremscasedifferentialsdriven
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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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  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.