Stochastic integrals for spde’s: A comparison
Copyright policy )Stochastic integrals for spde’s: A comparison
We present the Walsh theory of stochastic integrals with respect to martingale measures, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes and some other approaches to stochastic integration, and we explore the links between these theories. We then show how each theory can be used to study stochastic partial differential equations, with an emphasis on the stochastic heat and wave equations driven by spatially homogeneous Gaussian noise that is white in time. We compare the solutions produced by the different theories.
Mathematics(all), stochastic integral, stochastic partial differential equations, 60H15; 60H05, Stochastic integrals, Stochastic partial differential equation, Space, Dimensions, Existence, Cylindrical Wiener process, stochastic heat equation, spatially homogeneous Gaussian noise, Stochastic partial differential equations (aspects of stochastic analysis), Spatially homogeneous Gaussian noise, 60H05, FOS: Mathematics, martingale measure, Random field solution, Probability (math.PR), Wiener Process, Stochastic wave equation, Smoothness, Wave-Equation, Hilbert-space-valued Wiener process, Cauchy-Problem, Stochastic integral, 60H15, cylindrical Wiener process, Martingale measure, stochastic wave equation, Noise, Law, Mathematics - Probability, Stochastic heat equation
Mathematics(all), stochastic integral, stochastic partial differential equations, 60H15; 60H05, Stochastic integrals, Stochastic partial differential equation, Space, Dimensions, Existence, Cylindrical Wiener process, stochastic heat equation, spatially homogeneous Gaussian noise, Stochastic partial differential equations (aspects of stochastic analysis), Spatially homogeneous Gaussian noise, 60H05, FOS: Mathematics, martingale measure, Random field solution, Probability (math.PR), Wiener Process, Stochastic wave equation, Smoothness, Wave-Equation, Hilbert-space-valued Wiener process, Cauchy-Problem, Stochastic integral, 60H15, cylindrical Wiener process, Martingale measure, stochastic wave equation, Noise, Law, Mathematics - Probability, Stochastic heat equation
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