This book has its origin in the need of developing and analysing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure and asymptotic behaviour of stochastic processes.
This book has its origin in the need of developing and analysing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure and asymptotic behaviour of stochastic processes.
Florence Merlevède is Professor at the Laboratory of Analysis and Applied Mathematics of the University of Paris-Est. Her main research interests are in moment inequalities, deviations probability inequalities, limit theorems for partial sums associated to dependent processes, empirical processes but include also dynamical systems and random matrices Magda Peligrad is a distinguished Taft Professor in the Department of Mathematical Sciences of the University of Cincinnati whose area of expertise is Probability Theory and Stochastic Processes. Her research deals with dependent structures and covers various aspects of modelling the dependence, maximal inequalities, and limit theorems. Her research was rewarded by numerous National Science Foundation, National Security Agency, and Taft research center grants. In 1995 she was elected as fellow of the Institute of Mathematical Statistics, in 2003 she received the title of Taft Professor at the University of Cincinnati and in 2010 her contributions to Probability theory were recognized in a meeting held in her honor in Paris, France Sergey Utev is Professor in the Department of Mathematics of the University of Leicester. His area of expertise covers many aspects of Probability theory and their applications. In particular he wrote many important papers concerning mathematical inequalities and their applications, Quantum probability and stochastic comparisons, Stochastic processes with applications to Financial Mathematics, Actuarial Sciences and Epidemics
Inhaltsangabe
* 1: Introduction to Stochastic Processes * 2: Moment Inequalities and Gaussian Approximation for Martingales * 3: Moment Inequalities via Martingale Methods * 4: Gaussian Approximation via Martingale Methods * 5: Dependence coefficients for sequences * 6: Moment Inequalities and Gaussian Approximation for Mixing Sequences * 7: Weakly associated random variables : L2-bounds and approximation by independent structures * 8: Maximal moment inequalities for weakly negatively dependent variables * 9: Gaussian approximation under asymptotic negative dependence * 10: Examples of Stationary Sequences with Approximate Negative Dependence * 11: Stationary Sequences in a Random Time Scenery * 12: Linear Processes * 13: Random walk in random scenery * 14: Reversible Markov chains * 15: Functional central limit theorem for empirical processes * 16: Application to the uniform laws of large numbers for dependent processes * 17: Examples and Counterexamples
* 1: Introduction to Stochastic Processes * 2: Moment Inequalities and Gaussian Approximation for Martingales * 3: Moment Inequalities via Martingale Methods * 4: Gaussian Approximation via Martingale Methods * 5: Dependence coefficients for sequences * 6: Moment Inequalities and Gaussian Approximation for Mixing Sequences * 7: Weakly associated random variables : L2-bounds and approximation by independent structures * 8: Maximal moment inequalities for weakly negatively dependent variables * 9: Gaussian approximation under asymptotic negative dependence * 10: Examples of Stationary Sequences with Approximate Negative Dependence * 11: Stationary Sequences in a Random Time Scenery * 12: Linear Processes * 13: Random walk in random scenery * 14: Reversible Markov chains * 15: Functional central limit theorem for empirical processes * 16: Application to the uniform laws of large numbers for dependent processes * 17: Examples and Counterexamples
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