Theory and Applications of Stochastic Processes [electronic resource] : An Analytical Approach / by Zeev Schuss.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Applied Mathematical Sciences: 170Publisher: New York, NY : Springer New York, 2010Description: XVII, 468 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781441916051Subject(s): Mathematics | Mathematical models | Probabilities | Statistical physics | Dynamical systems | Applied mathematics | Engineering mathematics | Mathematics | Probability Theory and Stochastic Processes | Mathematical Modeling and Industrial Mathematics | Statistical Physics, Dynamical Systems and Complexity | Appl.Mathematics/Computational Methods of EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access online
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The Physical Brownian Motion: Diffusion And Noise -- The Probability Space of Brownian Motion -- It#x00F4; Integration and Calculus -- Stochastic Differential Equations -- The Discrete Approach and Boundary Behavior -- The First Passage Time of Diffusions -- Markov Processes and their Diffusion Approximations -- Diffusion Approximations to Langevin#x2019;s Equation -- Large Deviations of Markovian Jump Processes -- Noise-Induced Escape From an Attractor -- Stochastic Stability.
This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences. Its aim is to make probability theory readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and in asymptotic methods, rather than in probability and measure theory. It shows how to derive explicit expressions for quantities of interest by solving equations. Emphasis is put on rational modeling and approximation methods. The book includes many detailed illustrations, applications, examples and exercises. It will appeal to graduate students and researchers in mathematics, physics and engineering.