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Field name	Details
Dewey Class	530.15
Title	Random Processes for Classical Equations of Mathematical Physics ([EBook]) / by S. M. Ermakov, V. V. Nekrutkin, A. S. Sipin
Author	Ermakov, Sergei Mikhailovich
Added Personal Name	Nekrutkin, V. V.
Added Personal Name	Sipin, A. S.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 1989
Physical Details	XX, 282 p. : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 34
ISBN	9789400922433
Contents note	1. Markov Processes and Integral Equations -- 1.1. Breaking-off Markov chains and linear integral equations -- 1.2. Markov processes with continuous time and linear evolutionary equations -- 1.3. Convergent Markov chains and some boundary values problems -- 1.4. Markov chains and nonlinear integral equations -- 2. First Boundary Value Problem for the Equation of the Elliptic Type -- 2.1. Statement of the problem and notation -- 2.2. Green formula and the mean value theorem -- 2.3. Construction of a random process and an algorithm for the solution of the problem -- 2.4. Methods for simulation of a Markov chain -- 2.5. Estimation of the variance of a random variable ??? -- 3. Equations with Polynomial Nonlinearity -- 3.1. Preliminary examples and notation -- 3.2. Representation of solutions of integral equations with polynomial nonlinearity -- 3.3. Definition of probability measures and the simplest estimators -- 3.4. Probabilistic solution of nonlinear equations on measures -- 4. Probabilistic Solution of Some Kinetic Equations -- 4.1. Deterministic motion of particles -- 4.2. Computational aspects of the simulation of a collision process -- 4.3. Random trajectories of particles. The construction of the basic process -- 4.4. Collision processes -- 4.5. Auxiliary results -- 4.6. Lemmas on certain integral equations -- 4.7. Uniqueness of the solution of the (X, T?, H) equation -- 4.8. Probabilistic solution of the interior boundary value problem for the regularized Boltzmann equation -- 4.9. Estimation of the computational labour requirements -- 5. Various Boundary Value Problems Related to the Laplace Operator -- 5.1. Parabolic means and a solution of the mixed problem for the heat equation -- 5.2. Exterior Dirichlet problem for the Laplace equation -- 5.3. Solution of the Neumann problem -- 5.4. Branching random walks on spheres and the Dirichlet problem for the equation ?u = u2 -- 5.5. Special method for the solution of the Dirichlet problem for the Helmholtz equation -- 5.6. Probabilistic solution of the wave equation in the case of an infinitely differentiable solution -- 5.7. Another approach to the solution of hyperbolic equations -- 5.8. Probabilistic representation of the solution of boundary value problems for an inhomogeneous telegraph equation -- 5.9. Cauchy problem for the Schrödinger equation -- 6. Generalized Principal Value Integrals and Related Random Processes -- 6.1. Random processes related to linear equations -- 6.2. Nonlinear equations -- 6.3. On the representation of a solution of nonlinear equations as a generalized principal value integral -- 6.4. Principal part of the operator and the Monte Carlo method -- 7. Interacting Diffusion Processes and Nonlinear Parabolic Equations -- 7.1. Propagation of chaos and the law of large numbers -- 7.2. Interacting Markov processes and nonlinear equations. Heuristic considerations -- 7.3. Weakly interacting diffusions -- 7.4. Moderately interacting diffusions -- 7.5. On one method of numerical solution of systems of stochastic differential equations -- Bibliographical Notes -- References -- Additional References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-009-2243-3
Links to Related Works	Subject References: Mathematical Physics . Mathematics . Numeric Computing . Numerical Analysis . Physics . Theoretical, Mathematical and Computational Physics . Authors: author . Ermakov, Sergei Mikhailovich . Nekrutkin, V. V. . Sipin, A. S. . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 530.15 .

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Random Processes for Classical Equations of Mathematical Physics

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