Lower Complexity Bounds for Parametric Stochastic Itô Integration
نویسنده
چکیده
We study the complexity of pathwise approximation of parameter dependent stochastic Itô integration for Cr functions, with r ∈ R, r > 0. Both definite and indefinite integration are considered. This complements previous results [2] for classes of functions with dominating mixed smoothness. Upper bounds are obtained by embedding of function classes and applying some generalizations of these previous results. The emphasis of the present paper lies on lower bounds. While in [2] only nonadaptive deterministic algorithms were considered, we prove here lower bounds for adaptive deterministic and randomized algorithms, both for the classes considered here as for those from [2].
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