On the quasi-everywhere existence of the local time of the solution of a stochastic differential equation
type: Item
instance of: scholarly article
title: On the quasi-everywhere existence of the local time of the solution of a stochastic differential equation
zbMATH Open document ID: 0860.60037
author: Tu-Sheng Zhang
published in: Potential Analysis
publication date: 1996-09-25T00:00:00Z
review text: Let \(Y_t= x_0+\int^t_0\sigma(Y_s)dB_s+ \int^t_0b(Y_s)ds\) be a one-dimensional stochastic differential equation with coefficients \(b,\sigma\in C^2_b(\mathbb{R})\) and driving Brownian motion. The author proves the quasi-everywhere existence (the existence except for a set of zero capacity) of the local time of the solution \(Y\) provided either \(\sigma\) is uniformly positive or \(b=0\).
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 903388
zbMATH Keywords: local time
zbMATH Keywords: Ornstein-Uhlenbeck process
zbMATH Keywords: capacity
zbMATH Keywords: Brownian motion
reviewed by: Vigirdas Mackevičius
MaRDI profile type: Publication
Recommended article: On the solutions of stochastic differential equations involving the local times of the unknown processes
Recommended article: On a quasi everywhere existence of the local time of the 1-dimensional Brownian motion
Recommended article: On existence and local stability of solutions of stochastic differential equations
Recommended article: Existence and pathwise uniqueness of solutions for stochastic differential equations involving the local time at point zero
Recommended article: Q4248194
Recommended article: An Existence Theorem for a Solution of a Stochastic Differential Equation in a Locally Convex Space
Recommended article: Strong solutions of stochastic differential equations involving local times
Recommended article: A local-time correspondence for stochastic partial differential equations
description: scientific article; zbMATH DE number 903388