Generalized Diffusion Processes
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Author | : Nikola_ Ivanovich Portenko |
Publisher | : American Mathematical Soc. |
Total Pages | : 200 |
Release | : 1990-12-21 |
Genre | : Mathematics |
ISBN | : 9780821898260 |
Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for diffusion in a medium moving in a nonregular way. The author constructs generalized diffusion processes under two assumptions: first, that the diffusion matrix is sufficiently regular; and second, that the drift vector is a function integrable to some power, or is a generalized function of the type of the derivative of a measure.
Author | : Nikolaĭ Ivanovich Portenko |
Publisher | : |
Total Pages | : |
Release | : 1990 |
Genre | : Diffusion processes |
ISBN | : 9781470444969 |
Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for di.
Author | : Reginald P. Tewarson |
Publisher | : |
Total Pages | : 51 |
Release | : 1961 |
Genre | : Difference equations |
ISBN | : |
Author | : John Crank |
Publisher | : Oxford University Press |
Total Pages | : 428 |
Release | : 1979 |
Genre | : Mathematics |
ISBN | : 9780198534112 |
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Author | : Grigorios A. Pavliotis |
Publisher | : Springer |
Total Pages | : 345 |
Release | : 2014-11-19 |
Genre | : Mathematics |
ISBN | : 1493913239 |
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Author | : M. Nagasawa |
Publisher | : Birkhäuser |
Total Pages | : 335 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034885687 |
Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.
Author | : Y. Ogura |
Publisher | : |
Total Pages | : 47 |
Release | : 1986 |
Genre | : |
ISBN | : |
Author | : Merkel H. Jacobs |
Publisher | : Springer Science & Business Media |
Total Pages | : 165 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642864147 |
A basic tenet of present day biophysics is that flows in biological systems are causally related to forces. A large and growing fraction of membrane biophysics is devoted to an exploration of the quantitative relationship between forces and flows in order to understand both the nature of biological membranes and the processes that take place on and in these membranes. This is why the discussion of the nature of diffusion is so important in any formal development of membrane bio physics. This was equally true twenty years ago when tracers were just beginning to be used for the measurement of m.
Author | : Gopinath Kallianpur |
Publisher | : OUP Oxford |
Total Pages | : 368 |
Release | : 2014-01-09 |
Genre | : Mathematics |
ISBN | : 0191004529 |
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.
Author | : M. Iizuka |
Publisher | : |
Total Pages | : 34 |
Release | : 1990 |
Genre | : |
ISBN | : |
A conjecture on the convergence of diffusion models in population genetics to a simple Markov chain model is proved. The notion of bi-generalized diffusion processes and their limit theorems are used systematically to prove the conjecture. Three limits; strong selection - weak mutation limit, moderate selection - weak mutation limit, weak selection - weak mutation limit are considered for typical diffusion models in population genetics. (JES).