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This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

Stochastic analysis --- Space and time --- Martingales (Mathematics) --- Analyse stochastique --- Espace et temps --- Martingales (Mathématiques) --- Martingales (Mathématiques) --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

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This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

Electronic books. -- local. --- Martingales (Mathematics). --- Space and time. --- Stochastic analysis. --- Stochastic analysis --- Space and time --- Martingales (Mathematics) --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Analysis, Stochastic --- Mathematics. --- Game theory. --- Mathematical models. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Mathematical Modeling and Industrial Mathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Models, Mathematical --- Simulation methods --- Games, Theory of --- Theory of games --- Mathematical models --- Math --- Science --- Stochastic processes --- Mathematical analysis --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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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.

Statistical science --- Operational research. Game theory --- Mathematical statistics --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- kansrekening --- statistisch onderzoek --- Distribution (Probability theory. --- Mathematical statistics. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical analysis --- Statistical data --- Statistical methods --- Econometrics --- Markov processes. --- Probabilities. --- Statistics . --- Probability --- Combinations --- Chance --- Least squares --- Risk

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This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.

Statistical science --- Mathematics --- Operational research. Game theory --- Mathematical statistics --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- wiskunde --- kansrekening --- statistisch onderzoek

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Quantitative methods (economics) --- Operational research. Game theory --- Stochastic processes --- Financial analysis