低维贝塞尔过程的SDEs和路径相关扩展

Pub Date : 2022-11-09 DOI:10.30757/alea.v20-41

A. Ohashi, Francesco G. Russo, Alan Teixeira

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引用次数: 2

摘要

低维（0$\le$$\delta$$\le$1）中的贝塞尔过程不是It｛\^o｝过程，并且它仅在$\delta$=1和$\delta$=0的情况下是半鞅。在本文中，我们首先将其描述为具有分布漂移的SDE的唯一解，或者更准确地说，是其相关的鞅问题。在第二部分中，我们引入了路径相关贝塞尔过程的一个合适的概念，并将其描述为具有分布漂移的路径相关SDE的解。

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On SDEs for Bessel Processes in low dimension and path-dependent extensions

The Bessel process in low dimension (0 $\le$ $\delta$ $\le$ 1) is not an It{\^o} process and it is a semimartingale only in the cases $\delta$ = 1 and $\delta$ = 0. In this paper we first characterize it as the unique solution of an SDE with distributional drift or more precisely its related martingale problem. In a second part, we introduce a suitable notion of path-dependent Bessel processes and we characterize them as solutions of path-dependent SDEs with distributional drift.

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