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QA274 .G725 2013
Controlled stochastic processes
1979
Gikhman, I. I. (Iosif Ilʹich), 1918
Math & Statistics Library » QA274 .G5613
Random summation
1996
Gnedenko, B. V. (Boris Vladimirovich), 19121995
Math & Statistics Library » QA274 .G64 1996
Stochastic simulation and Monte Car...
2013
Graham, C. (Carl)
Math & Statistics Library » QA274 .G725 2013
Random processes
1985
Gray, Robert M., 1943
SAL3 (offcampus storage) » QA274 .G73 1986
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Stochastic simulation and Monte Carlo methods : mathematical foundations of stochastic simulation / Carl Graham, Denis Talay.
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QA274 .G725 2013
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QA274 .G725 2013
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Author/Creator:
Graham, C. (Carl),
author.
Language:
English.
Publication date:
2013
Publication:
Heidelberg : Springer, [2013]
Format:
Book
xvi, 260 pages : illustrations ; 24 cm.
Bibliography:
Includes bibliographical references (pages 253255) and index.
Contents:
Principles of Monte Carlo methods
Introduction
Why use probabilistic models and simulations?
What are the reasons for probabilistic models?
What are the objectives of random simulations?
Organization of the monograph
Strong law of large numbers and Monte Carlo methods
Strong law of large numbers, examples of Monte Carlo methods
Strong law of large numbers, almost sure convergence
Buffon's needle
Neutron transport simulations
Stochastic numerical methods for partial differential equations
Simulation algorithms for simple probability distributions
Uniform distributions
Discrete distributions
Gaussian distributions
Cumulative distribution function inversion, exponential distributions
Rejection method
Discretetime martingales, proof of the SLLN
Reminders on conditional expectation
Martingales and submartingales, backward martingales
Proof of the strong law of large numbers
Problems
Nonasymptotic error estimates for Monte Carlo methods
Convergence in law and characteristic functions
Central limit theorem
Asymptotic confidence intervals
BerryEsseen's theorem
Bikelis' theorem
Absolute confidence intervals
Concentration inequalities
Logarithmic Sobolev inequalities
Concentration inequalities, absolute confidence intervals
Elementary variance reduction techniques
Control variate
Importance sampling
Problems
Exact and approximate simulation of Markov processes
Poisson processes as particular Markov processes
Quick introduction to markov processes
Some issues in Markovian modeling
Rudiments on processes, sample paths, and laws
Poisson processes: characterization, properties
Point processes and poisson processes
Simple and strong markov property
Superposition and decomposition
Simulation and approximation
Simulation of interarrivals
Simulation of independent poisson processes
Long time or large intensity limit, applications
Problems
Discretespace markov processes
Characterization, specification, properties
Measures, functions, and transition matrices
Simple and strong Markov property
Semigroup, infinitesimal generator, and evolution law
Constructions, existence, simulation, equations
Fundamental constructions
Explosion or existence for a Markov process
Fundamental simulation, fictitious jump method
Kolmogorov equations, FeynmanKac formula
Generators and semigroups in bounded operator algebras
A few case studies
Problems
Continuousspace Markov processes with jumps
Preliminaries
Measures, functions, and transition kernels
Markov property, finitedimensional marginals
Semigroup, infinitesimal generator
Markov processes evolving only by isolated jumps
Semigroup, infinitesimal generator, and evolution law
Construction, simulation, existence
Kolmogorov equations, FeynmanKac formula, bounded generator case
Markov processes following an ordinary differential equation between jumps: PDMP
Sample paths, evolution, integrodifferential generator
Construction, simulation, existence
Kolmogorov equations, FeynmanKac formula
Application to kinetic equations
Further extensions
Problems
Discretization of stochastic differential equations
Reminders on Itô's stochastic calculus
Stochastic integrals and Itô processes
Itô's formula, existence and uniqueness of solutions of stochastic differential equations
Markov properties, martingale problems and Fokker Planck equations
Euler and Milstein schemes
Moments of the solution and of its approximations
Convergence rates in Lp (... ) norm and almost surely
Monte Carlo methods for parabolic partial differential equations
The principle of the method
Introduction of the error analysis
Optimal convergence rate : the TalayTubaro expansion
RombergRichardson extrapolation methods
Probabilistic interpretation and estimates for parabolic partial differential equations
Problems
Variance reduction, Girsanov's theorem, and stochastic algorithms
Variance reduction and stochastic differential equations
Preliminary reminders on the Girsanov theorem
Control variates method
Variance reduction for sensitivity analysis
Differentiable terminal conditions
Nondifferentiable terminal conditions
Importance sampling method
Statistical romberg method
Problems
Stochastic algorithms
Introduction
Study in an idealized framework
Definitions
The ordinary differential equation method, martingale increments
Longtime behavior of the algorithm
Variance reduction for Monte Carlo methods
Searching for an importance sampling
Variance reduction and stochastic algorithms
Problems
Appendix solutions to selected problems
References
Index.
Note:
Also issued online
Contributor:
Talay, D. (Denis),
author.
Available in another form:
9783642393631 (online)
(GyWOH)har135016798
Series:
Stochastic modelling and applied probability, 01724568 ; 68
Stochastic modelling and applied probability
68.
Subjects:
Stochastic processes.
Monte Carlo method.
ISBN:
3642393624
9783642393624
Catkey: 10220890
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