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

@article{Kirchner2017CovarianceSO,
  title={Covariance structure of parabolic stochastic partial differential equations with multiplicative L{\'e}vy noise},
  author={K. Kirchner and A. Lang and S. Larsson},
  journal={Journal of Differential Equations},
  year={2017},
  volume={262},
  pages={5896-5927}
}
The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative Levy 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. 

References

SHOWING 1-10 OF 35 REFERENCES
Covariance structure of parabolic stochastic partial differential equations
Sparse finite elements for elliptic problems with stochastic loading
Space-time adaptive wavelet methods for parabolic evolution problems
Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results
...
1
2
3
4
...