Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Aspects of Stochastic Integration with Respect to Processes of Unbounded p-variation (1407.5974v3)

Published 22 Jul 2014 in math.PR

Abstract: This paper deals with stochastic integrals of form $\int_0T f(X_u)d Y_u$ in a case where the function $f$ has discontinuities, and hence the process $f(X)$ is usually of unbounded $p$-variation for every $p\geq 1$. Consequently, integration theory introduced by Young or rough path theory introduced by Lyons cannot be applied directly. In this paper we prove the existence of such integrals in a pathwise sense provided that $X$ and $Y$ have suitably regular paths together with some minor additional assumptions. In many cases of interest, our results extend the celebrated results by Young.

Summary

We haven't generated a summary for this paper yet.