Theory of Probability and Mathematical Statistics
On martingale solutions of stochastic partial differential equations with L\'{e}vy noise
V. Mandrekar, U. V. Naik-Nimbalkar
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Abstract: We prove the uniqueness of martingale solutions for Hilbert space valued stochastic partial differential equations with L\'{e}vy noise generalizing the work in Mandrekar and Skorokhod (1998). The main idea used is to reduce this problem to that of a stochastic differential equation using the techniques introduced in Filipovi\'c et al.\ (2010). We do not assume the Lipschitz or the non-Lipschitz conditions for the coefficients of the equations.
Keywords: Stochastic partial differential equations, stochastic differential equations, compensated Poisson random measure, martingale solution, infinite dimensional
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