This manual provides comprehensive information on Stochastic Integrals, authored by H. P. McKean and edited by Z. W. Birnbaum and E. Lukacs. Published by Academic Press, this book is categorized under Applied Mathematics and Probability & Statistics. It is intended for academic and research use, particularly for economists, scientists, and researchers interested in probabilistic models and applied mathematics. The content focuses on diffusion processes and Brownian motion, offering a deep dive into differential and integral calculus based upon these concepts.
The scope of this manual is to detail key concepts such as Gaussian families, the construction of Brownian motion, and the martingale inequality. It covers the definition and properties of stochastic integrals by Wiener and Ito, the solution of stochastic differential equations, and various related theorems and methods including Lamperti's method, Feller's test for explosions, and Cameron-Martin's formula. Furthermore, it explores Brownian local time, Weyl's lemma, diffusions on manifolds, and Brownian motions on Lie groups and symmetric matrices, with specific examples like Brownian motion with oblique reflection.
Stochastic Integrals discusses one area of diffusion processes: the differential and integral calculus based upon the Brownian motion. The book reviews Gaussian families, construction of the Brownian motion, the simplest properties of the Brownian motion, Martingale inequality, and the law of the iterated logarithm. It also discusses the definition of the stochastic integral by Wiener and by Ito, the simplest properties of the stochastic integral according to Ito, and the solution of the simplest stochastic differential equation. The book explains diffusion, Lamperti's method, forward equation, Feller's test for the explosions, Cameron-Martin's formula, the Brownian local time, and the solution of dx=e(x) db + f(x) dt for coefficients with bounded slope. It also tackles Weyl's lemma, diffusions on a manifold, Hasminski's test for explosions, covering Brownian motions, Brownian motions on a Lie group, and Brownian motion of symmetric matrices. The book gives as example of a diffusion on a manifold with boundary the Brownian motion with oblique reflection on the closed unit disk of R squared. The text is suitable for economists, scientists, or researchers involved in probabilistic models and applied mathematics.
Author: McKean, H. P.
Editor: Birnbaum, Z. W.
Editor: Lukacs, E.
Publisher: Academic Press
Illustration: n
Language: ENG
Title: Stochastic Integrals
Pages: 00154 (Encrypted PDF)
On Sale: 2014-06-20
SKU-13/ISBN: 9781483230542
Category: Mathematics : Applied
Category: Mathematics : Probability & Statistics - General
Stochastic Integrals discusses one area of diffusion processes: the differential and integral calculus based upon the Brownian motion. The book reviews Gaussian families, construction of the Brownian motion, the simplest properties of the Brownian motion, Martingale inequality, and the law of the iterated logarithm. It also discusses the definition of the stochastic integral by Wiener and by Ito, the simplest properties of the stochastic integral according to Ito, and the solution of the simplest stochastic differential equation. The book explains diffusion, Lamperti's method, forward equation, Feller's test for the explosions, Cameron-Martin's formula, the Brownian local time, and the solution of dx=e(x) db + f(x) dt for coefficients with bounded slope. It also tackles Weyl's lemma, diffusions on a manifold, Hasminski's test for explosions, covering Brownian motions, Brownian motions on a Lie group, and Brownian motion of symmetric matrices. The book gives as example of a diffusion on a manifold with boundary the Brownian motion with oblique reflection on the closed unit disk of R squared. The text is suitable for economists, scientists, or researchers involved in probabilistic models and applied mathematics.
Author: McKean, H. P.
Editor: Birnbaum, Z. W.
Editor: Lukacs, E.
Publisher: Academic Press
Illustration: n
Language: ENG
Title: Stochastic Integrals
Pages: 00154 (Encrypted PDF)
On Sale: 2014-06-20
SKU-13/ISBN: 9781483230542
Category: Mathematics : Applied
Category: Mathematics : Probability & Statistics - General
