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Dieses ganzheitliches und verständliche Lehrbuch bietet eine ausgewogene Darstellung mathematischer Hintergründe und numerischer Methoden zur Analyse stochastischer Dynamik und Prozesse und enthält Zusatzmaterialien zu komplexeren Themen, praktische Übungen.

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The book introduces at a master s level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc. ) and Engineering, but also social sciences (Economy, Sociology, etc.

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Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models.

Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding.

From the contents:

Review of Probability Concepts
Monte Carlo Integration
Generation of Uniform and Non-uniform
Random Numbers: Non-correlated Values
Dynamical Methods
Applications to Statistical Mechanics
Introduction to Stochastic Processes
Numerical Simulation of Ordinary and
Partial Stochastic Differential Equations
Introduction to Master Equations
Numerical Simulations of Master Equations
Hybrid Monte Carlo
Generation of n-Dimensional Correlated
Gaussian Variables
Collective Algorithms for Spin Systems
Histogram Extrapolation
Multicanonical Simulations

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1. Review of Probability Concepts
2. Monte Carlo Integration
3. Generation of Non-uniform Random Numbers: Non-correlated Values
4. Dynamical Methods
5. Applications to Statistical Mechanics
6. Introduction to Stochastic Processes
7. Numerical Simulation of Stochastic Differential
equations
8.Introduction to Master Equations
9. Numerical Simulations of Master Equations
10. Hybrid Monte Carlo
11. Stochastic Partial Differential Equations
A. Generation of Uniform ^U (0;
1) Random Numbers
B. Generation of n-dimensional Correlated Gaussian
Variables
C. Calculation of the Correlation Function of a Series
D. Collective Algorithms for Spin Systems
E. Histogram Extrapolation
F. Multicanonical Simulations
G. Discrete Fourier Transform

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