Topics in Probability Theory: Seminar 1971-1972Daniel W. Stroock, S. R. S. Varadhan |
Contents
Weak Convergence of Stochastic Processes | 1 |
Strassens Version of the Law of the Iterated Logarithm | 15 |
Weak Convergence and the Invariance Principle | 33 |
Copyright | |
4 other sections not shown
Common terms and phrases
2n log log a₁ an+1 Bessel process Borel set bounded variation central limit theorem constant continuous martingale Corollary define denote Eole equivalent exists f₁ finite follows formula function f Gaussian H(P₁,P₂ Hence HP(B independent copy independent increment inequality integrable invariance principle ITÔ-MCKEAN ITO'S LEMMA large numbers Let F lim F lim sup limit distribution M₁,M₂ M₂ martingale on a,b martingale sequence MCKEAN measure s<t nonanticipating orthogonal P₁ P₂ path Prob probability space proof is finished Proof of Lemma Proof of Theorem Prop prove random variables reflecting Brownian motion relatively compact S. R. S. Varadhan satisfied Section standard Brownian motion Stochastic subset sup sup sup x(T t₁ topology tɅT weak convergence weak topology x,dy Әф Фј