Author: Alejandro D. de Acosta
Publisher: American Mathematical Soc.
ISBN: 0821890891
Category : Mathematics
Languages : en
Pages : 120
Book Description
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 for Additive Functionals of Markov Exhangeable Sequences
Author: Grant Izmirlian
Publisher:
ISBN:
Category :
Languages : en
Pages : 194
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 194
Book Description
Local Limit Theorems for Inhomogeneous Markov Chains
Author: Dmitry Dolgopyat
Publisher: Springer Nature
ISBN: 3031326016
Category : Mathematics
Languages : en
Pages : 348
Book Description
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
Publisher: Springer Nature
ISBN: 3031326016
Category : Mathematics
Languages : en
Pages : 348
Book Description
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
On the Large Deviation Functions of Markov Chains
Author: University of Minnesota. Institute for Mathematics and Its Applications
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
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 : 368
Book Description
Publisher:
ISBN:
Category : Large deviations
Languages : en
Pages : 368
Book Description
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.
Limit Theorems on Large Deviations for Markov Stochastic Processes
Author: A.D. Wentzell
Publisher: Springer
ISBN: 9789401073257
Category : Mathematics
Languages : en
Pages : 176
Book Description
One service mathematics has rendered the 'Et BIOi. .... si j'avait su comment en revenir. human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Math@matics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Publisher: Springer
ISBN: 9789401073257
Category : Mathematics
Languages : en
Pages : 176
Book Description
One service mathematics has rendered the 'Et BIOi. .... si j'avait su comment en revenir. human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Math@matics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Large Deviations of Uniformly Recurrent Markov Additive Processes
Author: I. Iscoe
Publisher:
ISBN:
Category :
Languages : en
Pages : 47
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 47
Book Description