Nonattainability of a set by a diffusion process
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- by Avner Friedman PDF
- Trans. Amer. Math. Soc. 197 (1974), 245-271 Request permission
Abstract:
Consider a system of n stochastic differential equations $d\xi = b(\xi )dt + \sigma (\xi )dw$. Let M be a k-dimensional submanifold in ${R^n},k \leq n - 1$. For $x \in M$, denote by $d(x)$ the rank of $\sigma {\sigma ^ \ast }$ restricted to the linear space of all normals to M at x. It is proved that if $d(x) \geq 2$ for all $x \in M$, then $\xi (t)$ does not hit M at finite time, given $\xi (0) \notin M$, i.e., M is nonattainable. The cases $d(x) \geq 1,d(x) \geq 0$ are also studied.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 197 (1974), 245-271
- MSC: Primary 60H10; Secondary 60J60
- DOI: https://doi.org/10.1090/S0002-9947-1974-0346903-7
- MathSciNet review: 0346903