Existence of unique solutions for SDEs for individual driving paths.
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Mon, 19/01/2009 14:15 |
Professor Sandy Davie (Edinburgh) |
Stochastic Analysis Seminar  |
Oxford-Man Institute |
| Existence and uniqueness theorems for (vector) stochastic differential equations dx=a(t,x)dt+b(t,x)dW are usually formulated at the level of stochastic processes. If one asks for such a result for an individual driving Brownian path W then there is a difficulty of interpretation.One solution to this is to use rough path theory, and in this context a uniqueness theorem can be proved (for a.e. W) for dx=b(x)dW if b has Holder continuous derivative. Another variant with a natural interpretation is dx=a(t,x)dt+dW where, if a is bounded Borel, uniqueness can be shown for a.e. W. The talk will explore the extent to which these two approaches can be combined. | |||