One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators
type: Item
instance of: scholarly article
title: One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators
zbMATH Open document ID: 1255.60092
author: Long Jiang
author: Shengjun Fan
published in: Statistics \& Probability Letters
publication date: 2012-09-21T00:00:00Z
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 6085254
zbMATH Keywords: backward stochastic differential equations
zbMATH Keywords: linear-growth generator
zbMATH Keywords: comparison theorem
zbMATH Keywords: Levi-type theorem
reviewed by: Andrew Dale
MaRDI profile type: Publication
full work available at URL: j.spl.2012.06.004
OpenAlex ID: W2047249864
cites work: LpSolutions of One-Dimensional Backward Stochastic Differential Equations with Continuous Coefficients
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cites work: \(L^p\) \((p>1)\) solutions for one-dimensional BSDEs with linear-growth generators
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DOI: 10.1016/J.SPL.2012.06.004
review text: The authors examine the backward stochastic differential equation NEWLINE\[NEWLINEy_t =\xi +\int^{T}_{t} g(s, y_{s}, z_{s})\, ds - \int^{T}_{t} z_{s}\, dB_{s}\,,\;\;\; t\in T.NEWLINE\]NEWLINE It is shown that if \(g\) is of linear growth in \((y,z)\) and if \(g(t,0,0)\) satisfies certain continuity conditions, then for each square-integrable terminal condition \(\xi\) the above equation has at least one solution, and such a solution is minimal. Levi- and comparison-type theorems are proved for the minimal solutions.
description: scientific article; zbMATH DE number 6085254