Random Perturbation Methods with Applications in Science and Engineering

• Κύριοι συγγραφείς: Skorokhod, Anatoli V. (Συγγραφέας), Hoppensteadt, Frank C. (Συγγραφέας), Salehi, Habib (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2002.
• Σειρά: Applied Mathematical Sciences, 150
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Probabilities.; Physics.; Mechanics.; Mechanics, Applied.; Probability Theory and Stochastic Processes.; Appl.Mathematics/Computational Methods of Engineering.; Analysis.; Applications of Mathematics.; Theoretical and Applied Mechanics.; Theoretical, Mathematical and Computational Physics.

 As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLAB-based computer simulations. This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems. 

 Ergodic Theorems -- Convergence Properties of Stochastic Processes -- Averaging -- Normal Deviations -- Diffusion Approximation -- Stability -- Markov Chains with Random Transition Probabilities -- Randomly Perturbed Mechanical Systems -- Dynamical Systems on a Torus -- Phase—Locked Loops -- Models in Population Biology -- Genetics.