Existence and uniqueness of a strong solution to stochastic differential equations in the plane with stochastic boundary process
type: Item
instance of: scholarly article
title: Existence and uniqueness of a strong solution to stochastic differential equations in the plane with stochastic boundary process
zbMATH Open document ID: 0673.60059
DOI: 10.1016/0047-259X(89)90101-2
author: S. H. Smith
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: On considère un mouvement brownien à deux paramètres sur \({\mathbb{R}}^ 2_+:Z\to B(z)\) \((z=(s,t)\in {\mathbb{R}}^ 2_+)\) et une équation différentielle stochastique dans le plan: \[ dX(z)=\alpha (z,X)dB(z)+\beta (z,X)dz\quad (z=(s,t)\in {\mathbb{R}}^ 2_+). \] Les auteurs étudient le problème de l'existence et de l'unicité d'une solution forte. L'article est à peu près ``self-contained''. Les auteurs donnent toutes les définitions nécessaires et les démonstrations sont détaillées.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 4102217
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: strong solutions
zbMATH Keywords: uniqueness in
zbMATH Keywords: probability distribution
zbMATH Keywords: pathwise uniqueness
zbMATH Keywords: regular conditional
zbMATH Keywords: probability
reviewed by: Albert Badrikian
MaRDI profile type: Publication
cites work: Stochastic integrals in the plane
cites work: Q3959169
cites work: Q5533878
cites work: Q4137851
cites work: Q4195714
cites work: Martingales and stochastic integrals for processes with a multi-dimensional parameter
cites work: On the uniqueness of solutions of stochastic differential equations
cites work: Existence of strong solutions for stochastic differential equations in the plane
cites work: Existence of Weak Solutions to Stochastic Differential Equations in the Plane with Continuous Coefficients
cites work: Q3736643
cites work: Uniqueness of strong solutions to stochastic differential equations in the plane with deterministic boundary process
description: scientific article; zbMATH DE number 4102217