\(L^{p} (p>1)\) solutions of backward stochastic differential equations with monotonic and uniformly continuous generators
type: Item
instance of: scholarly article
title: \(L^{p} (p>1)\) solutions of backward stochastic differential equations with monotonic and uniformly continuous generators
zbMATH Open document ID: 1272.60048
author: Ming Ma
author: Xing Song
author: Shengjun Fan
published in: Bulletin des Sciences Mathématiques
publication date: 2013-03-15T00:00:00Z
review text: Let \(p>1\). A one-dimensional backward stochastic differential equation \[ y_t=\xi+\int_t^Tg(s,y_s,z_s)\,ds-\int_t^Tz_s\cdot dB_s \] is considered, where \(\xi\) is a terminal condition in \(L^p\), the generator \(g(\omega,t,y,z)\) satisfies five hypotheses including continuity and monotonicity in \(y\) and uniform continuity in \(z\) and \(B\) is a \(d\)-dimensional Brownian motion. It is proved that the equation has a unique solution \((y,z)\) in the space \(L^p(\Omega;C[0,T])\times L^p(\Omega;L^2(0,T;\mathbb R^d))\). As a side result, a comparison principle is established for this equation.
reviewed by: Martin Ondreját
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 65C30
zbMATH DE Number: 6145426
zbMATH Keywords: backward stochastic differential equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: uniformly continuous generator
zbMATH Keywords: monotonic generator
zbMATH Keywords: \(L^p\) solution
MaRDI profile type: Publication
full work available at URL: j.bulsci.2012.06.005
OpenAlex ID: W2061464982
DOI: 10.1016/J.BULSCI.2012.06.005
description: scientific article; zbMATH DE number 6145426