Limit Theory for Mixing Dependent Random Variables

Preface. <strong>Part I: Introduction.</strong> <strong>1.</strong> Definitions and Basic Inequalities. <strong>2.</strong> Moment Estimations of Partial Sums. <strong>Part II: Weak Convergence.</strong> <strong>3.</strong> Weak Convergence for alpha-Mixing Sequences. <strong>4.</strong> Weak Convergence for rho-Mixing Sequences. <strong>5.</strong> Weak Convergence for phi-Mixing Sequences. <strong>6.</strong> Weak Convergence for Mixing Random Fields. <strong>7.</strong> The Berry-Esseen Inequality and the Rate of Weak Convergence. <strong>Part III:</strong> <strong>Almost Sure Convergence and Strong Approximations. 8.</strong> Laws of Large Numbers and Complete Convergence. <strong>9.</strong> Strong Approximations. <strong>10.</strong> The Increments of Partial Sums. <strong>11.</strong> Strong Approximations for Mixing Random Fields. <strong>Part IV: Statistics of a Dependent Sample.</strong> <strong>12.</strong> Empirical Processes. <strong>13.</strong> Convergence of Some Statistics with a Mixing Sample. <strong>14.</strong> Strong Approximations for Other Kinds of Dependent Random Variables. Appendix. References. Index.