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This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.

Anbieter: buecher

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Anbieter: buecher

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59,00 € *

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This thesis discusses Lévy processes and Lévy copulas. In connection with Lévy processes we treat some of the theory behind infinitely divisible distributions, acknowledging that the two classes are equivalent.Within the class of Lévy processes we will mostly look at stable processes and compound Poisson processes. The theory of Lévy processes dates back to the late 1920 s, after de Finetti first introduced the class of infinitely divisible distributions. Since then Lévy processes have become popular tools for modelling in finance, insurance and physics. Lévy copulas were introduced by Peter Tankov in 2003 in order to model dependency between different components of a multivariate Lévy process. In the last part of the book we present an application of Lévy copulas in non-life insurance and ruin theory of a Lévy copula. Through this example we will discuss aspects regarding estimation of the parameters and goodness of fit.

Anbieter: Dodax

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33,15 € *

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Anbieter: Dodax

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134,00 CHF *

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This book is intended as a text for a first course in stochastic processes at the upper undergraduate or graduate levels, assuming only that the reader has had a serious calculus course-advanced calculus would even be better-as well as a first course in probability (without measure theory). In guiding the student from the simplest classical models to some of the spatial models, currently the object of considerable research, the text is aimed at a broad audience of students in biology, engineering, mathematics, and physics. The first two chapters deal with discrete Markov chains-recurrence and tran sience, random walks, birth and death chains, ruin problem and branching pro cesses-and their stationary distributions. These classical topics are treated with a modem twist: in particular, the coupling technique is introduced in the first chap ter and is used throughout. The third chapter deals with continuous time Markov chains-Poisson process, queues, birth and death chains, stationary distributions. The second half of the book treats spatial processes. This is the main difference between this work and the many others on stochastic processes. Spatial stochas tic processes are (rightly) known as being difficult to analyze. The few existing books on the subject are technically challenging and intended for a mathemat ically sophisticated reader. We picked several interesting models-percolation, cellular automata, branching random walks, contact process on a tree-and con centrated on those properties that can be analyzed using elementary methods.

Anbieter: Orell Fuessli CH

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72,99 € *

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Anbieter: Thalia AT

Stand: 18.02.2020 Zum Angebot

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