On uniqueness of solutions to stochastic equations: a counter-example
| Autor: | H. J. Engelbert |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2002 |
| Předmět: |
Statistics and Probability
continuous local martingales Measurable function Stochastic process Mathematical analysis uniqueness in law Stochastic equations Combinatorics Real-valued function Burke's theorem Local martingale Increasing process Uniqueness 60H10 60G44 Statistics Probability and Uncertainty Martingale (probability theory) Mathematics |
| Zdroj: | Ann. Probab. 30, no. 3 (2002), 1039-1043 |
| Popis: | We consider the one-dimensional stochastic equation \[ X_t=X_0+\int^t_0 b(X_s)\,dM_s \] where M is a continuous local martingale and b a measurable real function. Suppose that $b^{-2}$ is locally integrable. D. N. Hoover asserted that, on a saturated probability space, there exists a solution X of the above equation with $X_0=0$ having no occupation time in the zeros of b and, moreover, the pair (X, M) is unique in law for all such X. We will give an example which shows that the uniqueness assertion fails, in general. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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