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Some results regarding stability of stochastic integrators

2020, arXiv: Probability

We consider limits for sequences of the type $\int Y_{-}df_n(X^n)$ and $[f_n(X^n)-f(X)]$ for semimartingale integrands, where $\{X^n\}_n$ either are Dirichlet processes or more generally processes admitting to quadratic variations. We here assume that the functions $\{f_n\}_n$ are either $C^1$ or absolutely continuous. We also provide important examples of how to apply this theory for sequential jump removal.

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