Author: Grant Izmirlian
Publisher:
ISBN:
Category :
Languages : en
Pages : 194
Book Description
Large Deviations for Additive Functionals of Markov Exhangeable Sequences
Large Deviations for Additive Functionals of Markov Chains
Author: Alejandro D. de Acosta
Publisher: American Mathematical Soc.
ISBN: 0821890891
Category : Mathematics
Languages : en
Pages : 120
Book Description
Publisher: American Mathematical Soc.
ISBN: 0821890891
Category : Mathematics
Languages : en
Pages : 120
Book Description
Large Deviations for Markov Chains
Author: Alejandro D. de Acosta
Publisher:
ISBN: 1009063359
Category : Mathematics
Languages : en
Pages : 264
Book Description
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Publisher:
ISBN: 1009063359
Category : Mathematics
Languages : en
Pages : 264
Book Description
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Large Deviations
Author: Frank Hollander
Publisher: American Mathematical Soc.
ISBN: 9780821844359
Category : Mathematics
Languages : en
Pages : 164
Book Description
Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Publisher: American Mathematical Soc.
ISBN: 9780821844359
Category : Mathematics
Languages : en
Pages : 164
Book Description
Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Large Deviations and Applications
Author: S. R. S. Varadhan
Publisher: SIAM
ISBN: 0898711894
Category : Mathematics
Languages : en
Pages : 74
Book Description
Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Publisher: SIAM
ISBN: 0898711894
Category : Mathematics
Languages : en
Pages : 74
Book Description
Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Large Deviations
Author: S. R. S. Varadhan
Publisher: American Mathematical Soc.
ISBN: 082184086X
Category : Mathematics
Languages : en
Pages : 114
Book Description
The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
Publisher: American Mathematical Soc.
ISBN: 082184086X
Category : Mathematics
Languages : en
Pages : 114
Book Description
The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
Asymptotics of Large Deviations for I.I.D. and Markov Additive Random Variables in R[superscript D]
Author: Michael George Iltis
Publisher:
ISBN:
Category : Large deviations
Languages : en
Pages : 450
Book Description
Publisher:
ISBN:
Category : Large deviations
Languages : en
Pages : 450
Book Description
Large Deviations of Uniformly Recurrent Markov Additive Processes
Dirichlet Forms and Symmetric Markov Processes
Author: Masatoshi Fukushima
Publisher: Walter de Gruyter
ISBN: 3110218097
Category : Mathematics
Languages : en
Pages : 501
Book Description
This book contains an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms. Moreover this analytic theory is unified with the probabilistic potential theory based on symmetric Markov processes and developed further in conjunction with the stochastic analysis based on additive functional. Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revised the existing text, but also added sections on capacities and Sobolev type inequalities, irreducible recurrence and ergodicity, recurrence and Poincaré type inequalities, the Donsker-Varadhan type large deviation principle, as well as several new exercises with solutions. The book addresses to researchers and graduate students who wish to comprehend the area of Dirichlet forms and symmetric Markov processes.
Publisher: Walter de Gruyter
ISBN: 3110218097
Category : Mathematics
Languages : en
Pages : 501
Book Description
This book contains an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms. Moreover this analytic theory is unified with the probabilistic potential theory based on symmetric Markov processes and developed further in conjunction with the stochastic analysis based on additive functional. Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revised the existing text, but also added sections on capacities and Sobolev type inequalities, irreducible recurrence and ergodicity, recurrence and Poincaré type inequalities, the Donsker-Varadhan type large deviation principle, as well as several new exercises with solutions. The book addresses to researchers and graduate students who wish to comprehend the area of Dirichlet forms and symmetric Markov processes.
Abstracts of Papers Presented to the American Mathematical Society
Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 604
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 604
Book Description