On the pathwise uniqueness of solutions of stochastic differential equations driven by multi-dimensional symmetric \(\alpha\) stable class (Q862141)
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scientific article; zbMATH DE number 5121922
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the pathwise uniqueness of solutions of stochastic differential equations driven by multi-dimensional symmetric \(\alpha\) stable class |
scientific article; zbMATH DE number 5121922 |
Statements
On the pathwise uniqueness of solutions of stochastic differential equations driven by multi-dimensional symmetric \(\alpha\) stable class (English)
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5 February 2007
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Pathwise uniqueness is proved for solutions of the system of stochastic differential equations \[ dY(t)= \sigma(Y(t-)) dZ(t),\quad Y(0)= Y_0, \] where \(Z\) is a \(d\)-dimensional symmetric \(\alpha\) stable process such that \(d\geq 2\) and \(1< \alpha< 2\). An example is presented to demonstrate that in a certain sense the key hypothesis required for the proof cannot be improved upon.
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