JOINT MATHEMATICS COLLOQUIUMUNIVERSITY OF IDAHOWASHINGTON STATE UNIVERSITY |
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Abstract |
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| Studying differential equations using
stochastic analysis has become extremely useful and popular in the
recent years; e.g. in fluid mechanics, financial mathematics,
biological mathematics. We review basic notions of stochastic
differential equations (SDE) from probability theory: filtered
probability space, Brownian motion, martingale, integral with respect
to Brownian motion, Ito's isometry and Ito's formula. If time permits,
we discuss the notion of "weak and strong solution to SDE,''
analogously to the "weak and strong solution to deterministic
(classical) PDEs'' which interestingly require applications of
Prokhorov and Skorokhod's theorems in some cases such as the stochastic
Navier-Stokes equations.
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