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# đź“™ Large deviations for additive functionals of Markov chains by Alejandro D. De Acosta, Peter Ney â€” pdf free

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For a Markov chain {X?} with general state space S and f:S?R ?, the large deviation principle for {n ?1 ? ??=1 f(X?)} is proved under a condition on the chain which is weaker than uniform recurrence but stronger than geometric recurrence and an integrability condition on f , for a broad class of initial distributions. This result is extended to the case when f takes values in a separable Banach space. Assuming only geometric ergodicity and under a non-degeneracy condition, a local large deviation result is proved for bounded f. A central analytical tool is the transform kernel, whose required properties, including new results, are established. The rate function in the large deviation results is expressed in terms of the convergence parameter of the transform kernel

## About book:

## About file:

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- Series:
**Memoirs of the American Mathematical Society 1070** - Author:
**Alejandro D. De Acosta, Peter Ney** - Year:
**2014** - Publisher:
**Amer Mathematical Society** - Language:
**English** - ISBN:
**0821890891,978-0-8218-9089-9**

- File size:
**706 930** - Format:
**pdf**

Security code:

The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that a...

In recent years the significance of Gaussian processes to communication networks has grown considerably. The inherent flexibility of the Gaussian traffic model enables the analysis, in a single mathematical framework, of systems with both long-range and s...

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is a time-continu...

Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may...

Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may...

Meyn & Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation alg...

Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may...

Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may...

The purpose of this book is to present the theory of general irreducible Markov chains and to point out the connection between this and the Perron-Frobenius theory of nonnegative operators. The author begins by providing some basic material designed to ma...