On SDEs for Bessel Processes in low dimension and pathdependent extensions

Alberto Ohashi; Francesco Russo; Alan Teixeira

doi:10.30757/ALEA.v20-41

On SDEs for Bessel Processes in low dimension and pathdependent extensions

Alberto Ohashi
, Francesco Russo
, Alan Teixeira

Research output: Contribution to journal › Article › peer-review

Abstract

The Bessel process in low dimension (0 ≤ δ ≤ 1) is not an Itô process and it is a semimartingale only in the cases δ = 1 and δ = 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.

Original language	English
Pages (from-to)	1111-1138
Number of pages	28
Journal	Alea (Rio de Janeiro)
Volume	20
DOIs	https://doi.org/10.30757/ALEA.v20-41
Publication status	Published - 1 Jan 2023

Keywords

Bessel processes
Path-dependent stochastic differential equations
SDEs with distributional drift

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10.30757/ALEA.v20-41

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N2 - The Bessel process in low dimension (0 ≤ δ ≤ 1) is not an Itô process and it is a semimartingale only in the cases δ = 1 and δ = 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.

AB - The Bessel process in low dimension (0 ≤ δ ≤ 1) is not an Itô process and it is a semimartingale only in the cases δ = 1 and δ = 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.

KW - Bessel processes

KW - Path-dependent stochastic differential equations

KW - SDEs with distributional drift

U2 - 10.30757/ALEA.v20-41

DO - 10.30757/ALEA.v20-41

M3 - Article

AN - SCOPUS:85172242370

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EP - 1138

JO - Alea (Rio de Janeiro)

JF - Alea (Rio de Janeiro)

ER -

On SDEs for Bessel Processes in low dimension and pathdependent extensions

Abstract

Keywords

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