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

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-11-09 DOI:10.30757/alea.v20-41

A. Ohashi, Francesco G. Russo, Alan Teixeira

引用次数: 2

Abstract

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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低维贝塞尔过程的SDEs和路径相关扩展

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.