Covariance structure of parabolic stochastic partial differential equations with multiplicative Lévy noise

Abstract

The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative Lévy noise of affine type. For the second moment of the mild solution, a well-posed deterministic space-time variational problem posed on projective and injective tensor product spaces is derived, which subsequently leads to a deterministic equation for the covariance function.

28 pages

References in corpus (1)

• Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs

Cited by in corpus (7)

• Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions
• Regularity theory for a new class of fractional parabolic stochastic evolution equations
• Approximation of SPDE covariance operators by finite elements: A semigroup approach
• Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs
• Malliavin regularity and weak approximation of semilinear SPDE with Lévy noise
• Monte Carlo convergence rates for $k$th moments in Banach spaces
• Spectral approximation of a new class of stochastic fractional evolution equations