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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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What phenomena are better modelled by SDE instead of ODE?
Brownian motion is an obvious example. Brownian motion described particles dispersed in a liquid that are large enough that the random jossling of the water molecules becomes important. Being one of t …