Seminar series
Date
Mon, 19 Jan 2009
14:15
14:15
Location
Oxford-Man Institute
Speaker
Professor Sandy Davie
Organisation
Edinburgh
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.