One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators (Q451158)
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scientific article; zbMATH DE number 6085254
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators |
scientific article; zbMATH DE number 6085254 |
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One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators (English)
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21 September 2012
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backward stochastic differential equations
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linear-growth generator
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comparison theorem
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Levi-type theorem
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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.
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