Articlegold2005

Existence, Uniqueness and Regularity of Parabolic SPDEs Driven by Poisson Random Measure

66 citations0/0 files storedElectronic Journal of Probability

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Differential Equations and Boundary Problems

Abstract

In this paper we investigate SPDEs in certain Banach spaces driven by a Poisson random measure. We show existence and uniqueness of the solution, investigate certain integrability properties and verify the cadlag property.

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References

1983Stochastic Differential Equations and Diffusion Processes 2003Limit Theorems for Stochastic Processes 2006An introduction to stochastic partial differential equations 1997The Euler scheme for Lévy driven stochastic differential equations 2002Stochastic Integration with Jumps 1995Stochastic differential equations in infinite-dimensional spaces 1981Stochastic Integration and $L^p$-Theory of Semimartingales 1997Stochastic Differential Equations in Infinite Dimensional Spaces

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2007The 1-d stochastic wave equation driven by a fractional Brownian sheet 2008Maximal regularity for stochastic convolutions driven by Lévy processes 2006SPDEs driven by Poisson random measure with non Lipschitz coefficients: existence results 2012Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise 2006Itô formula for stochastic integrals w.r.t. compensated Poisson random measures on separable Banach spaces

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