Introduction. 1. Preliminaries. 1. Stationary Sequence (Mixing Conditions, Basic Inqualities). 2. Wiener Process (increment Theory). 3. Skorokhod Theorem. 4. Martingale Convergence Theorem and Goal-Koksme Strong Law of Large Numbers. 5. Moricz Exponent Inequality.2. I.I.D.R.V. 1. Strassen Strong Invariance Principle. 2. Improvement of the Rate of Convergence. 3. The Best Rate, K-M-T Theorem. 4. Increments of Partial Sums. 3. Independent Non-Identically Distributed R.V. 1. Strong Approximations of Partial Sums by Wiener Process. 2. Increments of Partial Sums. 4. Stationary Sequence. 1. Basic Method and its Improvement. 2. Strong Approximations of (alphabeta-Mixing Sequence. 3. Mixing Rate and Approximation Remainder Term. 4. Strong Approximations of alpha(pi)-Mixing Sequence. 5. Strong Approximations of Functions of Mixing Sequence. 6. Increments of Partial Sums for phi-Mixing Sequence. 5. Strong Approximations of Other Kinds of Dependent Sequence and Statistics. 1. Lacunary Trigonometric Series. 2. Gaussian Sequence. 3. Additive Functional of Markov Process. 4. U-Statistics. 5. Estimators of Error Variance. 6. Miscellany.
This volume presents an up-to-date review of the most significant developments in strong Approximation and strong convergence in probability theory. The book consists of three chapters. The first deals with Wiener and Gaussian processes. Chapter 2 is devoted to the increments of partial sums of independent random variables. Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Ornstein-Uhlenbeck processes. For researchers whose work involves probability theory and statistics.
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