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On the analysis of path-dependent functionals of stochastic PDEs
Weak approximation methods for stochastic partial differential equations (SPDEs) are concerned with approximating the probability distribution of the solution process rather than the realizations of the solution process itself. In this thesis, we provide new results and methods concerning the weak error analysis of numerical approximations of path-dependent functionals of solution processes of SPDEs. Two separate approaches to analyzing weak approximation errors are considered: the Itô calculus approach and the ...