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| Author | : Anatolij V. Skorochod |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 192 |
| Release | : 2019-01-14 |
| Genre | : Mathematics |
| ISBN | : 3110618168 |
No detailed description available for "Lectures on the Theory of Stochastic Processes".
| Author | : Kiyosi Ito |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 246 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662100657 |
This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.
| Author | : Jean-Claude Falmagne |
| Publisher | : McGraw-Hill Science, Engineering & Mathematics |
| Total Pages | : 296 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : |
Designed for undergraduate mathematics students or graduate students in the sciences. This book can be used in a prerequisite course for Statistics (for math majors) or Mathematical Modeling. The first eighteen chapters could be used in a one-quarter course, and the entire text is suitable for a one-semester course.
| Author | : Richard Durrett |
| Publisher | : Springer |
| Total Pages | : 282 |
| Release | : 2016-11-07 |
| Genre | : Mathematics |
| ISBN | : 3319456148 |
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.
| Author | : Alexander Shapiro |
| Publisher | : SIAM |
| Total Pages | : 447 |
| Release | : 2009-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898718759 |
Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
| Author | : Sheldon M. Ross |
| Publisher | : John Wiley & Sons |
| Total Pages | : 549 |
| Release | : 1995-02-28 |
| Genre | : Mathematics |
| ISBN | : 0471120626 |
A nonmeasure theoretic introduction to stochastic processes. Considers its diverse range of applications and provides readers with probabilistic intuition and insight in thinking about problems. This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments; a new chapter on Poisson approximations; and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs. Numerous exercises and problems have been added throughout the text.
| Author | : Rene Carmona |
| Publisher | : SIAM |
| Total Pages | : 263 |
| Release | : 2016-02-18 |
| Genre | : Mathematics |
| ISBN | : 1611974240 |
The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.
| Author | : Robert G. Gallager |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 146152329X |
Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.
| Author | : Günter Last |
| Publisher | : Cambridge University Press |
| Total Pages | : 315 |
| Release | : 2017-10-26 |
| Genre | : Mathematics |
| ISBN | : 1107088011 |
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
| Author | : Simon Tavaré |
| Publisher | : Springer |
| Total Pages | : 320 |
| Release | : 2004-01-30 |
| Genre | : Mathematics |
| ISBN | : 3540398740 |
This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). Simon Tavaré’s lectures serve as an introduction to the coalescent, and to inference for ancestral processes in population genetics. The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. Ofer Zeitouni’s course on "Random Walks in Random Environment" presents systematically the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension, the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. Olivier Catoni's course appears separately.
