Stochastic numerical methods : an introduction for students and scientists /: an introduction for students and scientists. (©2014)

• Record Type: Book
• Further Information: Note: Raúl Toral, and Pere Colet.
• Other Names: Toral, Raúl; Colet, Pere
• Contents: Stochastic Numerical Methods; Contents; Preface; Chapter 1 Review of probability concepts; 1.1 Random Variables; 1.2 Average Values, Moments; 1.3 Some Important Probability Distributions with a Given Name; 1.3.1 Bernoulli Distribution; 1.3.2 Binomial Distribution; 1.3.3 Geometric Distribution; 1.3.4 Uniform Distribution; 1.3.5 Poisson Distribution; 1.3.6 Exponential Distribution; 1.3.7 Gaussian Distribution; 1.3.8 Gamma Distribution; 1.3.9 Chi and Chi-Square Distributions; 1.4 Successions of Random Variables; 1.5 Jointly Gaussian Random Variables. 1.6 Interpretation of the Variance: Statistical Errors1.7 Sums of Random Variables; 1.8 Conditional Probabilities; 1.9 Markov Chains; Further Reading and References; Exercises; Chapter 2 Monte Carlo Integration; 2.1 Hit and Miss; 2.2 Uniform Sampling; 2.3 General Sampling Methods; 2.4 Generation of Nonuniform Random Numbers: Basic Concepts; 2.5 Importance Sampling; 2.6 Advantages of Monte Carlo Integration; 2.7 Monte Carlo Importance Sampling for Sums; 2.8 Efficiency of an Integration Method; 2.9 Final Remarks; Further Reading and References; Exercises. Chapter 3 Generation of Nonuniform Random Numbers: Noncorrelated Values3.1 General Method; 3.2 Change of Variables; 3.3 Combination of Variables; 3.3.1 A Rejection Method; 3.4 Multidimensional Distributions; 3.5 Gaussian Distribution; 3.6 Rejection Methods; Further Reading and References; Exercises; Chapter 4 Dynamical Methods; 4.1 Rejection with Repetition: a Simple Case; 4.2 Statistical Errors; 4.3 Dynamical Methods; 4.4 Metropolis et al. Algorithm; 4.4.1 Gaussian Distribution; 4.4.2 Poisson Distribution; 4.5 Multidimensional Distributions; 4.6 Heat-Bath Method; 4.7 Tuning the Algorithms. Further Reading and ReferencesExercises; Chapter 6 Introduction to Stochastic Processes; 6.1 Brownian Motion; 6.2 Stochastic Processes; 6.3 Stochastic Differential Equations; 6.4 White Noise; 6.5 Stochastic Integrals. Itô and Stratonovich Interpretations; 6.6 The Ornstein-Uhlenbeck Process; 6.6.1 Colored Noise; 6.7 The Fokker-Planck Equation; 6.7.1 Stationary Solution; Further Reading and References; Exercises; Chapter 7 Numerical Simulation of Stochastic Differential Equations; 7.1 Numerical Integration of Stochastic Differential Equations with Gaussian White Noise; 7.1.1 Integration Error.
• Publisher Details: Weinheim, Germany : Wiley-VCH
• Publication Date: 2014
• Copyright Date: 2014
• Extent: 1 online resource (xvi, 402 pages)
• Subjects: 511.8; Numerical analysis; Stochastic analysis; Stochastic control theory; MATHEMATICS -- Applied; MATHEMATICS -- Probability & Statistics -- General; Numerical analysis; Stochastic analysis; Stochastic control theory; Electronic books
• Languages: English
• ISBNs: 1306907977; 9781306907972; 9783527683147; 3527683143; 9783527683130; 3527683135; 3527411496; 9783527411498; 3527683127; 9783527683123; 3527683119; 9783527683116
• Related ISBNs: 9783527411498; 9783527683123; 9783527683116
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (Wiley, viewed June 18, 2014).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.