Diffusion Processes, Jump Processes, and Stochastic Differential Equations
1st Edition
Published on 8. March 2022
138 pages
978-1-000-47537-1 (ISBN)
Description
Diffusion Processes, Jump Processes, and Stochastic Differential Equations provides a compact exposition of the results explaining interrelations between di?usion stochastic processes, stochastic di?erential equations and the fractional in?nitesimal operators. The draft of this book has been extensively classroom tested by the author at Case Western Reserve University in a course that enrolled seniors and graduate students majoring in mathematics, statistics, engineering, physics, chemistry, economics and mathematical ?nance. The last topic proved to be particularly popular among students looking for careers on Wall Street and in research organizations devoted to ?nancial problems.
Features
Quickly and concisely builds from basic probability theory to advanced topics
Suitable as a primary text for an advanced course in diffusion processes and stochastic differential equations
Useful as supplementary reading across a range of topics.
Features
Quickly and concisely builds from basic probability theory to advanced topics
Suitable as a primary text for an advanced course in diffusion processes and stochastic differential equations
Useful as supplementary reading across a range of topics.
More details
Edition
1. Auflage
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Product notice
Reflowable
Illustrations
1 Tables, black and white; 16 Line drawings, color; 16 Illustrations, color
ISBN-13
978-1-000-47537-1 (9781000475371)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Wojbor A. Woyczynski
Diffusion Processes, Jump Processes, and Stochastic Differential Equations
Book
05/2024
1st Edition
Chapman & Hall/CRC
€81.80
Shipment within 10-20 days
Wojbor A. Woyczynski
Diffusion Processes, Jump Processes, and Stochastic Differential Equations
Book
03/2022
1st Edition
Chapman & Hall/CRC
€141.30
Shipment within 10-20 days
Person
Wojbor A. Woyczynski was a mathematics and statistics professor, who was born and educated in Poland. He earned his M.Sc. in Electrical and Computer Engineering at Wroclaw University of Technology in 1966, and his Ph.D. in Mathematics, at the University of Wroclaw in 1968, when he was 23 years old. He spent most of his career teaching at Case Western Reserve University in Cleveland, Ohio, USA where he started working in 1982, when he was hired as chair of the Department of Mathematics and Statistics. He published over 160 papers and many books, including this, his 18th book, delving into a wide array of topics in mathematics. His research interests stretched from mainstream probability theory, to mathematical physics and turbulence theory, operations research and financial mathematics, to mathematical biology. In 1992 he published a monograph on "Random Series and Stochastic Integrals", co-written with Stanis law Kwapien. The paper "Levy Flights in Evolutionary Ecology," co-written with two French mathematicians, Sylvie Meleard and Benjamin Jourdain, won the 2013 prize La Recherche for the best work in the field of mathematics. He published a number of works honoring the great mathematicians of preceding generations. Early in his career, in 1986, he was elected as a Fellow of the Institute of Mathematics. He served as an editorial board member of Probability and Mathematical Statistics, Annals of Applied Probability, and Stochastic Processes and Their Applications. This book was published posthumously, with the consent of his family.
Content
1. Random variables, vectors, processes and fields. 1.1. Random variables, vectors, and their distributions - a glossary. 1.2. Law of Large Numbers and the Central Limit Theorem. 1.3. Stochastic processes and their finite-dimensional distributions. 1.4. Problems and Exercises. 2. From Random Walk to Brownian Motion. 2.1. Symmetric random walk; parabolic rescaling and related Fokker-Planck equations. 2.2 Almost sure continuity of sample paths. 2.3 Nowhere differentiability of Brownian motion. 2.4 Hitting times, and other subtle properties of Brownian motion. 2.5. Problems and Exercises. 3. Poisson processes and their mixtures. 3.1. Why Poisson process? 3.2. Covariance structure and finite dimensional distributions. 3.3. Waiting times and inter-jump times. 3.4. Extensions and generalizations. 3.5. Fractional Poisson processes (fPp). 3.6. Problems and Exercises. 4. Levy processes and the Levy-Khinchine formula: basic facts. 4.1. Processes with stationary and independent increments. 4.2. From Poisson processes to Levy processes. 4.3. Infinitesimal generators of Levy processes. 4.4. Selfsimilar Levy processes. 4.5. Properties of ?-stable motions. 4.6. Infinitesimal generators of ?-stable motions. 4.7. Problems and Exercises. 5. General processes with independent increments. 5.1. Nonstationary processes with independent increments. 5.2. Stochastic continuity and jump processes. 5.3. Analysis of jump structure. 5.4. Random measures and random integrals associated with jump processes. 5.5. Structure of general I.I. processes. 5.6. Problems and Exercises. 6. Stochastic integrals for Brownian motion and general Levy Processes. 6.1. Wiener random integral. 6.2. Ito's stochastic integral for Brownian motion. 6.3. An instructive example. 6.4. Ito's formula. 6.5. Martingale property of Ito integrals. 6.6. Wiener and Ito-type stochastic integrals for ?-stable motion and general Levy processes. 6.7. Problems and Exercises. 7. Ito stochastic differential equations. 7.1. Differential equations with random noise. 7.2. Stochastic differential equations: Basic theory. 7.3. SDEs with coefficients depending only on time. 7.4. Population growth model and other examples. 7.5. Ornstein-Uhlenbeck process. 7.6. Systems of SDEs and vector-valued Ito's formula. 7.7. Kalman-Bucy filter. 7.8. Numerical solution of stochastic differential equations. 7.9. Problems and Exercises. 8. Asymmetric exclusion processes and their scaling limits. 8.1. Asymmetric exclusion principles. 8.2. Scaling limit. 8.3. Other queuing regimes related to non-nearest neighbor systems. 8.4. Networks with multiserver nodes and particle systems with state-dependent rates. 8.5. Shock and rarefaction wave solutions for the Riemann problem for conservation laws. 8.6. Problems and Exercises. 9. Nonlinear diffusion equations. 9.1. Hyperbolic equations. 9.2. Nonlinear diffusion approximations. 9.3. Problems and Exercises
