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Local Limit Theorems for Inhomogeneous Markov Chains

Posted By: AvaxGenius
Local Limit Theorems for Inhomogeneous Markov Chains

Local Limit Theorems for Inhomogeneous Markov Chains by Dmitry Dolgopyat , Omri M. Sarig
English | PDF | 2023 | 348 Pages | ISBN : 3031326008 | 10 MB

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.

Random Evolutionary Systems: Asymptotic Properties and Large Deviations

Posted By: AvaxGenius
Random Evolutionary Systems: Asymptotic Properties and Large Deviations

Random Evolutionary Systems: Asymptotic Properties and Large Deviations by Dmitri Koroliouk, Igor Samoilenko
English | PDF(True) | 2021 | 303 Pages | ISBN : 1786307529 | 3.52 MB

Within the field of modeling complex objects in natural sciences, which considers systems that consist of a large number of interacting parts, a good tool for analyzing and fitting models is the theory of random evolutionary systems, considering their asymptotic properties and large deviations. In Random Evolutionary Systems we consider these systems in terms of the operators that appear in the schemes of their diffusion and the Poisson approximation. Such an approach allows us to obtain a number of limit theorems and asymptotic expansions of processes that model complex stochastic systems, both those that are autonomous and those dependent on an external random environment. In this case, various possibilities of scaling processes and their time parameters are used to obtain different limit results.

Séminaire de Probabilités LI

Posted By: AvaxGenius
Séminaire de Probabilités LI

Séminaire de Probabilités LI by Catherine Donati-Martin
English | EPUB | 2022 | 408 Pages | ISBN : 3030964086 | 23.8 MB

This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs.