Theory of Probability and Mathematical Statistics
An addendum to “Mild solutions to semilinear stochastic partial differential equations with locally monotone coefficients”
Stefan Tappe
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Abstract: In this addendum we provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures in the framework of the semigroup approach with locally monotone coefficients, where the semigroup is allowed to be pseudo-contractive. This improves an earlier paper of the author, where the equation was only driven by Wiener processes, and where the semigroup was only allowed to be a semigroup of contractions.
Keywords: Stochastic partial differential equation, variational approach, semigroup approach, pseudo-contractive semigroup, mild solution, monotonicity condition, coercivity condition
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