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Titlebook: Stochastic Simulation and Monte Carlo Methods; Mathematical Foundat Carl Graham,Denis Talay Textbook 2013 Springer-Verlag Berlin Heidelberg

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Carl Graham,Denis Talayerformance of Voice UserInterfaces, new front-end algorithms for the coding/decoding of effective andcomputationally efficient acoustic and linguistic speech representations, aswell as investigations capturing 978-3-319-80274-9978-3-319-28109-4Series ISSN 2190-3018 Series E-ISSN 2190-3026
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Textbook 2013and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical underta
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Continuous-Space Markov Processes with Jumpstions and Feynman–Kac formula are established. This is applied to kinetic equations coming from statistical Mechanics. These describe the time evolution of the instantaneous distribution of particles in phase space (position-velocity), when the particle velocity jumps at random instants in function of the particle position and velocity.
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Discretization of Stochastic Differential Equationsential equations with smooth coefficients define stochastic flows, and we prove some properties of such flows. We are then in a position to prove an optimal convergence rate result for the discretization schemes.
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Variance Reduction and Stochastic Differential Equations, the construction of an effective method often lies on the approximation of a perfect method, the approximation method needing to be adapted to each particular case. Interesting examples can be found in Duffie and Glynn (Ann. Appl. Probab. 5(4), 897–905, .).
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