Muutke küpsiste eelistusi

E-raamat: Diffusion Processes, Jump Processes, and Stochastic Differential Equations [Taylor & Francis e-raamat]

(Case Western Reserve University, Cleveland, Ohio USA)
  • Formaat: 138 pages, 1 Tables, black and white; 16 Line drawings, color; 16 Illustrations, color
  • Ilmumisaeg: 21-Mar-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003216759
Teised raamatud teemal:
  • Taylor & Francis e-raamat
  • Hind: 133,87 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 191,24 €
  • Säästad 30%
Diffusion Processes, Jump Processes, and Stochastic Differential EquationsSuurem pilt
  • Formaat: 138 pages, 1 Tables, black and white; 16 Line drawings, color; 16 Illustrations, color
  • Ilmumisaeg: 21-Mar-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003216759
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003216759
"Diffusion Processes, Jump Processes, and Stochastic Differential Equations provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, stochastic differential equations and the fractional infinitesimal 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 finance. The last topic proved to be particularly popular among students looking for careers on Wall Street and in research organizations devoted to financial problems. Features Quickly and concisely builds from basic probability theoryto 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. Table of Contents"--

This book provides a compact exposition of the results explaining interrelations between di usion stochastic processes, SDEs and the fractional in nitesimal operators. The draft of this book has been extensively classroom tested by the author at CWRU in a course that enrolled seniors and graduate students.



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.

Author xi
Chapter 1 Random Variables, Vectors, Processes, and Fields
1(10)
1.1 Random Variables, Vectors, And Their Distributions-A Glossary
1(6)
1.1.1 Basic Concepts
1(2)
1.1.2 Absolutely Continuous, Discrete, Mixed, And Singular Probability Distributions
3(1)
1.1.3 Characteristic Functions, Laplace Transforms, And Moment-Generating Functions
3(1)
1.1.4 Examples
4(3)
1.2 Law Of Large Numbers And The Central Limit Theorem
7(2)
1.3 Stochastic Processes And Their Finite-Dimensional Distributions
9(1)
1.4 Problems And Exercises
10(1)
Chapter 2 From Random Walk To Brownian Motion
11(32)
2.1 Symmetric Random Walk; Parabolic Rescaling And Related Fokker-Planck Equations
11(5)
2.1.1 Brownian Motion As Hydrodynamic Limit Of Random Walks
11(3)
2.1.2 Brownian Motion Via The Central Limit Theorem And The Invariance Principle
14(2)
2.2 Basic Properties Of Brownian Motion
16(2)
2.3 Almost Sure Continuity Of Sample Paths
18(3)
2.4 Nowhere Differentiability Of Brownian Motion
21(2)
2.5 Hitting Times, And Other Subtle Properties Of Brownian Motion
23(1)
2.6 Problems And Exercises
24(3)
3.1 Why Poisson Process?
27(2)
3.2 Covariance Structure And Finite Dimensional Distributions
29(1)
3.3 Waiting Times And Inter-Jump Times
30(4)
3.4 Extensions And Generalizations
34(1)
3.5 Fractional Poisson Processes (Fpp)
35(7)
3.5.1 Fpp Interarrival Time
35(7)
3.6 Problems And Exercises
42(1)
Chapter 4 Levy Processes And The Levy-Khinchine Formula: Basic Facts
43(10)
4.1 Processes With Stationary And Independent Increments
43(1)
4.2 From Poisson Processes To Levy Processes
44(2)
4.3 Infinitesimal Generators Of Levy Processes
46(1)
4.4 Self-Similar Levy Processes
47(1)
4.5 Properties Of A-Stable Motions
48(2)
4.6 Infinitesimal Generators Of A-Stable Motions
50(1)
4.7 Problems And Exercises
51(2)
Chapter 5 General Processes With Independent Increments
53(12)
5.1 Nonstationary Processes With Independent Increments
53(2)
5.2 Stochastic Continuity And Jump Processes
55(2)
5.3 Analysis Of Jump Structure
57(1)
5.4 Random Measures And Random Integrals Associated With Jump Processes
58(1)
5.4.1 Random Measures And Random Integrals
58(1)
5.5 Structure Of General I.I. Processes
59(6)
Chapter 6 Stochastic Integrals For Brownian Motion And General Levy Processes
65(12)
6.1 Wiener Random Integral
65(1)
6.2 Ito's Stochastic Integral For Brownian Motion
66(4)
6.3 An Instructive Example
70(1)
6.4 Ito's Formula
71(2)
6.5 Martingale Property Of Ito Integrals
73(1)
6.6 Wiener And Ito-Type Stochastic Integrals For A-Stable Motion And General Levy Processes
74(3)
Chapter 7 Ito Stochastic Differential Equations
77(14)
7.1 Differential Equations With Noise
77(2)
7.2 Stochastic Differential Equations: Basic Theory
79(5)
7.3 Sdes With Coefficients Depending Only On Time
84(1)
7.4 Population Growth Model And Other Examples
85(1)
7.4.1 Population Growth Model
85(1)
7.4.2 Ornstein-Uhlenbeck Process
86(1)
7.5 Systems Of Sdes And Vector-Valued Ito's Formula
86(3)
7.6 Numerical Solution Of Stochastic Differential Equations
89(2)
Chapter 8 Asymmetric Exclusion Processes And Their Scaling Limits
91(16)
8.1 Asymmetric Exclusion Principles
91(1)
8.2 Scaling Limit
92(1)
8.3 Other Queuing Regimes Related To Non-Nearest Neighbor Systems
93(4)
8.4 Networks With Multiserver Nodes And Particle Systems With State-Dependent Rates
97(5)
8.5 Shock And Rarefaction Wave Solutions For The Riemann Problem For Conservation Laws
102(5)
Chapter 9 Nonlinear Diffusion Equations
107(8)
9.1 Hyperbolic Equations
107(2)
9.2 Nonlinear Diffusion Approximations
109(4)
9.3 Nonlinear Processes
113(1)
9.4 Interacting Diffusions And Monte-Carlo Methods
114(1)
Appendix A: The Remarkable Bernoulli Family 115(4)
Bibliography 119(4)
Index 123
Wojbor A. Woyczyski 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 Kwapie. The paper Lévy Flights in Evolutionary Ecology, co-written with two French mathematicians, Sylvie Méléard 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.
Püsilink: https://www.kriso.ee/db/9781003216759_pe.html
Märksõnad: