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The General Theory of Stochastic Processes
Predictable crField Predictable Times
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absolute continuity adapted process apply assume assumption belongs C-tight cadlag cadlag function Chapter characteristics compensator consider converges in law Corollary countable D(Ud defined definition denote dense subset density process deterministic equivalence evanescent set exists filtration finite variation finite-dimensional convergence fixed function h Girsanov's Theorem Hellinger process hence holds hypothesis implies increasing process independent increments inf(t Jacod jumps Lemma lim sup limit theorems limiting process locally bounded martingale problem measure on Q Moreover nonnegative notation obtain obviously point process Poisson process predictable process probability measure probability space Proof of Theorem Proposition random measure random variables recall relative remains to prove resp result satisfies Section semimartingale Skorokhod topology square-integrable stochastic basis stochastic integral suffices to prove sufficient condition suppose teU+ tight trivial truncation function uniformly integrable uniqueness weakly Wiener process yields