Local Limit Theorems For Inhomogeneous Markov Chains
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Author | : Dmitry Dolgopyat |
Publisher | : Springer Nature |
Total Pages | : 348 |
Release | : 2023-07-31 |
Genre | : Mathematics |
ISBN | : 3031326016 |
Download Local Limit Theorems for Inhomogeneous Markov Chains Book in PDF, Epub and Kindle
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.
Author | : Hubert Hennion |
Publisher | : Springer |
Total Pages | : 150 |
Release | : 2003-07-01 |
Genre | : Mathematics |
ISBN | : 3540446230 |
Download Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness Book in PDF, Epub and Kindle
The usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.
Author | : V. A. Statulyavicus |
Publisher | : |
Total Pages | : 8 |
Release | : 1956 |
Genre | : |
ISBN | : |
Download On a Local Limit Theorem for Inhomogenous Markov Chains Book in PDF, Epub and Kindle
Author | : United States. National Bureau of Standards |
Publisher | : |
Total Pages | : 276 |
Release | : 1963 |
Genre | : Mathematical physics |
ISBN | : |
Download Journal of Research of the National Bureau of Standards Book in PDF, Epub and Kindle
Author | : Marius Iosifescu |
Publisher | : Courier Corporation |
Total Pages | : 305 |
Release | : 2007-06-05 |
Genre | : Mathematics |
ISBN | : 0486458695 |
Download Finite Markov Processes and Their Applications Book in PDF, Epub and Kindle
Self-contained treatment covers both theory and applications. Topics include the fundamental role of homogeneous infinite Markov chains in the mathematical modeling of psychology and genetics. 1980 edition.
Author | : Xia Chen |
Publisher | : American Mathematical Soc. |
Total Pages | : 225 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 082181060X |
Download Limit Theorems for Functionals of Ergodic Markov Chains with General State Space Book in PDF, Epub and Kindle
This book is intended for graduate students and research mathematicians working probability theory and statistics.
Author | : Sara Anna van de Geer |
Publisher | : |
Total Pages | : 26 |
Release | : 2003 |
Genre | : |
ISBN | : |
Download Local Limit Theorems for Transition Densities of Markov Chains Converging to Diffusions with Unbounded Drift Book in PDF, Epub and Kindle
Author | : Hubert Hennion |
Publisher | : |
Total Pages | : 162 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662205389 |
Download Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness Book in PDF, Epub and Kindle
Author | : Reinhard Höpfner |
Publisher | : American Mathematical Soc. |
Total Pages | : 105 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082183231X |
Download Limit Theorems for Null Recurrent Markov Processes Book in PDF, Epub and Kindle
Author | : Joseph P. LaSalle |
Publisher | : |
Total Pages | : 344 |
Release | : 1962 |
Genre | : Mathematicians |
ISBN | : |
Download Recent Soviet Contributions to Mathematics Book in PDF, Epub and Kindle