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＜電子ブック＞
Modeling with Itô Stochastic Differential Equations / by E. Allen
(Mathematical Modelling: Theory and Applications ; 22)

版	1st ed. 2007.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	XII, 230 p : online resource
著者標目	*Allen, E author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematics LCSH:Mathematical analysis LCSH:Mathematical models LCSH:Mathematics -- Data processing  全ての件名で検索 FREE:Probability Theory FREE:Applications of Mathematics FREE:Analysis FREE:Mathematical Modeling and Industrial Mathematics FREE:Computational Mathematics and Numerical Analysis
一般注記	Random Variables -- Stochastic Processes -- Stochastic Integration -- Stochastic Differential Equations -- Modeling Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained. This modeling procedure is thoroughly explained and illustrated for randomly varying systems in population biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation. Computer programs, given throughout the text, are useful in solving representative stochastic problems. Analytical and computational exercises are provided in each chapter that complement the material in the text. Modeling with Itô Stochastic Differential Equations is useful for researchers and graduate students. As a textbook for a graduate course, prerequisites include probability theory, differential equations, intermediate analysis, and some knowledge of scientific programming HTTP:URL=https://doi.org/10.1007/978-1-4020-5953-7

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