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Weak Convergence of Stochastic Processes
Strassens Version of the Law of the Iterated Logarithm
Weak Convergence and the Invariance Principle
4 other sections not shown
2n log log absolutely continuous Bessel process Borel set bounded variation central limit theorem conjugate harmonic function continuous martingale Corollary corresponding define denote easily EQ[e equivalent exists extension of f fact finite follows formula Gaussian harmonic extension Hence HP(S implies independent copy indicator function integrable invariance principle ITO-MCKEAN large numbers law of large Let F lim sup limit distribution martingale on a,b martingale sequence MCKEAN measure Moreover non-negative nonanticipating function nondecreasing orthogonal path Prob probability space proof is finished Proof of Lemma Proof of Theorem Prop prove random variables reflecting Brownian motion relatively compact Remark satisfies the conditions Section separable metric space standard Brownian motion Stochastic stopping subset sup sup sup x(t t e a,b tdm(t topology totally bounded uniformly weak convergence weak topology