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＜電子ブック＞
Random Processes for Classical Equations of Mathematical Physics / by S.M. Ermakov, V.V. Nekrutkin, A.S. Sipin
(Mathematics and its Applications, Soviet Series ; 34)

版	1st ed. 1989.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1989
本文言語	英語
大きさ	XX, 282 p : online resource
著者標目	*Ermakov, S.M author Nekrutkin, V.V author Sipin, A.S author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Numerical analysis FREE:Mathematical Physics FREE:Numerical Analysis FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-94-009-2243-3

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