Theory of Probability and Mathematical Statistics
Mild solutions to semilinear stochastic partial differential equations with locally monotone coefficients
S. Tappe
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Abstract: We provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations in the framework of the semigroup approach with locally monotone coefficients. An important component of the proof is an application of the dilation theorem of Nagy, which allows us to reduce the problem to infinite dimensional stochastic differential equations on a larger Hilbert space. Properties of the solutions like the Markov property are discussed as well.
Keywords: Stochastic partial differential equation, mild solution, monotonicity condition, coercivity condition, Markov property
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