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"This 1996 book is a comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin has used the powerful interplay between the probabilistic structure (independence and stationarity of the increments) and analytic tools (especially Fourier and Laplace transforms) to give a quick and concise treatment of the core theory, with the minimum of technical requirements. Special properties of subordinators are developed and then appear as key features in the study of the local times of real-valued Lévy processes and in fluctuation theory. Lévy processes with no positive jumps receive special attention, as do stable processes. In sum, this will become the standard reference on the subject for all working probability theorists." [Back cover]

Lévy processes --- Lévy processes --- Lévy, Processus de --- Stochastic processes --- Lévy processes. --- Lévy, Processus de. --- Markov processes. --- Markov, Processus de.

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Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Lévy processes --- Stochastic analysis --- Lévy, Processus de --- Analyse stochastique --- Lévy processes. --- Stochastic analysis. --- Lévy processes --- Lévy, Processus de --- Lévy processes. --- Stochastic integral equations. --- Integral equations --- Random walks (Mathematics) --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes

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Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.

Stochastic processes. --- Lévy processes. --- Mathematical physics. --- Physical mathematics --- Physics --- Random walks (Mathematics) --- Random processes --- Probabilities --- Mathematics --- Stochastischer Prozess --- Rauschen.

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Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. For the first time in a book, Applebaum ties the two subjects together. He begins with an introduction to the general theory of Lévy processes. The second part develops the stochastic calculus for Lévy processes in a direct and accessible way. En route, the reader is introduced to important concepts in modern probability theory, such as martingales, semimartingales, Markov and Feller processes, semigroups and generators, and the theory of Dirichlet forms. There is a careful development of stochastic integrals and stochastic differential equations driven by Lévy processes. The book introduces all the tools that are needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem.

Stochastic processes --- Lévy processes --- Stochastic analysis --- 519.22 --- Analysis, Stochastic --- Mathematical analysis --- Random walks (Mathematics) --- Lévy processes. --- Stochastic analysis. --- Lévy processes.

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Markov processes. --- Holonomy groups. --- Lie groups. --- Yang-Mills theory. --- Lévy processes. --- Markov, Processus de. --- Groupes d'holonomie. --- Lie, Groupes de. --- Yang-Mills theory --- Yang-Mills, Théorie de. --- Lévy processes. --- Lévy, Processus de.