A convolution formula for the local time of an Itô diffusion reflecting at 0 and a generalized Stroock-Williams equation
type: Item
instance of: scholarly article
title: A convolution formula for the local time of an Itô diffusion reflecting at 0 and a generalized Stroock-Williams equation
zbMATH Open document ID: 1479.60164
DOI: 10.3150/20-BEJ1295
author: Jacek Jakubowski
author: Maciej Wiśniewolski
published in: Bernoulli
publication date: 2021-07-09T00:00:00Z
review text: The authors develop a new probabilistic insight into the structure of local time of Itô diffusions. They particularly obtain a convolution formula for the local time at zero for Itô diffusions reflecting at zero. They derive a simple integro-differential equation for the cumulative distribution function of the local time. The authors also derive a probabilistic representation of a generalized Stroock-Williams equation.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 7370732
zbMATH Keywords: excursions of Markov processes
zbMATH Keywords: Itô diffusion
zbMATH Keywords: local time
zbMATH Keywords: Stroock-Williams equation
reviewed by: Pavel Gapeev
MaRDI profile type: Publication
cites work: Q4265385
cites work: Q3150773
cites work: Singular stochastic differential equations.
cites work: Stochastic differential equations for sticky Brownian motion
cites work: Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process
cites work: The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes
cites work: Q4086524
cites work: Excursions of a Markov process
cites work: Excursions of Brownian motion and bessel processes
cites work: Excursions of dual processes
cites work: A survey and some generalizations of Bessel processes
cites work: Q4771944
cites work: FEYNMAN–KAC FORMULAS FOR BLACK–SCHOLES-TYPE OPERATORS
cites work: Q4002114
cites work: On Linear Volterra Integral Equations of Convolution Type
cites work: Exit systems
cites work: Q3261651
cites work: Q5649197
cites work: Q3262469
cites work: A peculiar two point boundary value problem
cites work: A probabilistic solution to the Stroock-Williams equation
cites work: Q4663402
cites work: A Guided Tour through Excursions
cites work: Q3763296
cites work: On the excursion theory for linear diffusions
cites work: A simple PDE and Wiener‐Hopf Riccati equations
cites work: Further study of a simple PDE
cites work: Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I
cites work: Indefinite inner products: a simple illustrative example
full work available at URL: 20-bej1295
OpenAlex ID: W3162918634
describes a project that uses: Digital Library of Mathematical Functions
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description: scientific article; zbMATH DE number 7370732