\(L^p\) solutions to backward stochastic differential equations with discontinuous generators (Q1950655)
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scientific article; zbMATH DE number 6162699
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^p\) solutions to backward stochastic differential equations with discontinuous generators |
scientific article; zbMATH DE number 6162699 |
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\(L^p\) solutions to backward stochastic differential equations with discontinuous generators (English)
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13 May 2013
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The existence of an \(L^p\) solution is proved for the backward stochastic differential equation \[ Y_t= \xi+ \int^T_t g(s,Y_s, Z_s)\,ds- \int^T_t Z_s\cdot dB_s,\quad 0\leq t\leq T, \] where \(g(t,y,z)\) is discontinuous (but right continuous) in \(y\) and uniformly continuous in \(z\), and \(B\) is a \(d\)-dimensional Brownian motion.
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backward stochastic differential equations
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existence theorem
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\(L^{p}\) solution
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uniformly continuous condition
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