Random Processes for Classical Equations of Mathematical Physics

Language: English

Published by Springer, Springer Okt 1989, 1989

079230036X / 9780792300366

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 304 pp. Englisch.…

Seller Inventory # 9780792300366

Title
Random Processes for Classical Equations of Mathematical Physics
Author
S. M. Ermakov
Publisher
Springer, Springer Okt 1989
Publication year
1989
Condition
Neu
Binding
Buch
Language
English
ISBN 10
079230036X
ISBN 13
9780792300366
Item weight
1,063 grams
Dimensions
303x215x22 mm

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