Stochastic Numerical Methods

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 Engineeri [...]
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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 ConceptsMonte Carlo IntegrationGeneration of Uniform and Non-uniformRandom Numbers: Non-correlated ValuesDynamical MethodsApplications to Statistical MechanicsIntroduction to Stochastic ProcessesNumerical Simulation of Ordinary andPartial Stochastic Differential EquationsIntroduction to Master EquationsNumerical Simulations of Master EquationsHybrid Monte CarloGeneration of n-Dimensional CorrelatedGaussian VariablesCollective Algorithms for Spin SystemsHistogram ExtrapolationMulticanonical Simulations