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SOME MATHEMATICAL PRELIMINARIES
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answer apply approximate assume Borel bounded Brownian motion called Chapter choose coincides combinations condition consider constant continuous function Corollary corresponding define DEFINITION denotes depend Dirichlet problem distribution Dynkin Dynkin's formula estimate example exists exit expectation filtering problem function given gives hand Hence holds important independent infinitesimal interpretation introduction Ito diffusion Ito formula Ito integral Lemma limit linear majorant martingale mathematical matrix mean measurable n-dimensional noise normal Note o-algebra observations obtain operator optimal stopping probability problem Proof prove question random variable reasonable regular REMARK result reward satisfies sense situation solution solve space starting Step stochastic differential equation stochastic integral stochastic process strong superharmonic supermeanvalued Suppose Theorem theory uniqueness