Mark Iosifovich Freidlin's Books

This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

Eugene B. Dynkin published his first paper, on Markov chain theory, whilst still an undergraduate student at Moscow State University. He went on to make fundamental contributions to the theory of Markov processes and to Lie groups, generating entire schools in these areas.

The authors' main tools are the large deviation theory the centred limit theorem for stochastic processes, and the averaging principle - all presented in great detail. The results allow for explicit calculations of the asymptotics of many interesting characteristics of the perturbed system.

Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.

Book's by Mark Iosifovich Freidlin

Functional Integration and Partial Differential Equations. (AM-109), Volume 109

Functional Integration and Partial Differential Equations. (AM-109), Volume 109

Functional Integration and Partial Differential Equations. (AM-109), Volume 109

Functional Integration and Partial Differential Equations. (AM-109), Volume 109

Functional Integration and Partial Differential Equations

Functional Integration and Partial Differential Equations

The Dynkin Festschrift

The Dynkin Festschrift

Random Perturbations of Dynamical Systems

Random Perturbations of Dynamical Systems

Random Perturbations of Hamiltonian Systems

Random Perturbations of Hamiltonian Systems

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