A Historical Introduction.- Probability Concepts.- Markov Processes.- The Ito Calculus and Stochastic Differential Equations.- The Fokker-Planck Equation.- The Fokker-Planck Equation in Several Dimensions.- Small Noise Approximations for Diffusion Processes.- The White Noise Limit.- Beyond the White Noise Limit.- Lévy Processes and Financial Applications.- Master Equations and Jump Processes.- The Poisson Representation.- Spatially Distributed Systems.- Bistability, Metastability, and Escape Problems.- Simulation of Stochastic Differential Equations.
A Historical Introduction.- Probability Concepts.- Markov Processes.- The Ito Calculus and Stochastic Differential Equations.- The Fokker-Planck Equation.- The Fokker-Planck Equation in Several Dimensions.- Small Noise Approximations for Diffusion Processes.- The White Noise Limit.- Beyond the White Noise Limit.- Lévy Processes and Financial Applications.- Master Equations and Jump Processes.- The Poisson Representation.- Spatially Distributed Systems.- Bistability, Metastability, and Escape Problems.- Simulation of Stochastic Differential Equations.
This volume includes the five lecture courses given at the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from...
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This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of...
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