Random Processes for Classical Equations of Mathematical Physics [electronic resource] /
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.
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Format: | Texto biblioteca |
Language: | eng |
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Dordrecht : Springer Netherlands,
1989
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Subjects: | Mathematics., Numerical analysis., Mathematical physics., Physics., Mathematical Physics., Numeric Computing., Theoretical, Mathematical and Computational Physics., |
Online Access: | http://dx.doi.org/10.1007/978-94-009-2243-3 |
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KOHA-OAI-TEST:1970072018-07-30T23:22:52ZRandom Processes for Classical Equations of Mathematical Physics [electronic resource] / Ermakov, S. M. author. Nekrutkin, V. V. author. Sipin, A. S. author. SpringerLink (Online service) textDordrecht : Springer Netherlands,1989.eng1. 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.Mathematics.Numerical analysis.Mathematical physics.Physics.Mathematics.Mathematical Physics.Numeric Computing.Theoretical, Mathematical and Computational Physics.Springer eBookshttp://dx.doi.org/10.1007/978-94-009-2243-3URN:ISBN:9789400922433 |
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Mathematics. Numerical analysis. Mathematical physics. Physics. Mathematics. Mathematical Physics. Numeric Computing. Theoretical, Mathematical and Computational Physics. Mathematics. Numerical analysis. Mathematical physics. Physics. Mathematics. Mathematical Physics. Numeric Computing. Theoretical, Mathematical and Computational Physics. |
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Mathematics. Numerical analysis. Mathematical physics. Physics. Mathematics. Mathematical Physics. Numeric Computing. Theoretical, Mathematical and Computational Physics. Mathematics. Numerical analysis. Mathematical physics. Physics. Mathematics. Mathematical Physics. Numeric Computing. Theoretical, Mathematical and Computational Physics. Ermakov, S. M. author. Nekrutkin, V. V. author. Sipin, A. S. author. SpringerLink (Online service) Random Processes for Classical Equations of Mathematical Physics [electronic resource] / |
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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. |
format |
Texto |
topic_facet |
Mathematics. Numerical analysis. Mathematical physics. Physics. Mathematics. Mathematical Physics. Numeric Computing. Theoretical, Mathematical and Computational Physics. |
author |
Ermakov, S. M. author. Nekrutkin, V. V. author. Sipin, A. S. author. SpringerLink (Online service) |
author_facet |
Ermakov, S. M. author. Nekrutkin, V. V. author. Sipin, A. S. author. SpringerLink (Online service) |
author_sort |
Ermakov, S. M. author. |
title |
Random Processes for Classical Equations of Mathematical Physics [electronic resource] / |
title_short |
Random Processes for Classical Equations of Mathematical Physics [electronic resource] / |
title_full |
Random Processes for Classical Equations of Mathematical Physics [electronic resource] / |
title_fullStr |
Random Processes for Classical Equations of Mathematical Physics [electronic resource] / |
title_full_unstemmed |
Random Processes for Classical Equations of Mathematical Physics [electronic resource] / |
title_sort |
random processes for classical equations of mathematical physics [electronic resource] / |
publisher |
Dordrecht : Springer Netherlands, |
publishDate |
1989 |
url |
http://dx.doi.org/10.1007/978-94-009-2243-3 |
work_keys_str_mv |
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