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Summary. Developed from the author's course at the Ecole Polytechnique, Monte​-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses.
Table of contents

Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Kloeden , Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients , Ann. Jentzen , P.

SIAM Journal on Numerical Analysis

Kloeden , and A. Neuenkirch , Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients , Numer. A comprehensive course; Translated from the German original. MR [46] P. Kloeden and A. Neuenkirch , The pathwise convergence of approximation schemes for stochastic differential equations , LMS J. MR [48] Kruse, R. Optimal error estimates of Galerkin finite element methods for stochastic partical differential equations with multiplicative noise.

Stochastic transient of a noisy von der Pol oscillator. Physica A , — With Mathematica code. Differential Equations , no. Determinisitic nonperiodic flow.

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Undamped oscillations derived from the law of mass action. Strong convergence rates for backward Euler-Maruyama method for nonlinear dissipative-type stochastic differential equations with super-linear diffusion coefficients. Stochastics Stochastics Rep. Palermo 2 4 , 48— MR [59] J.

Mattingly , A. Stuart , and D. MR [61] G. Milstein , Numerical integration of stochastic differential equations , Mathematics and its Applications, vol. Translated and revised from the Russian original. MR [62] G. Milstein , E. Platen , and H.

Milstein and M. MR [67] Prigogine, I. Symmetry breaking instabilities in dissipative systems ii. Phys 48 , — Protter , Stochastic integration and differential equations , 2nd ed. Stochastic Modelling and Applied Probability. MR [69] Gareth O. Roberts and Richard L.

Tweedie , Exponential convergence of Langevin distributions and their discrete approximations , Bernoulli 2 , no. Theory Relat. Fields 72 , no. A stochastic theory of phase transitions in human hand movements. MR [76] Henri Schurz , An axiomatic approach to numerical approximations of stochastic processes , Int.

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators? MR [80] Tyson, J. Some further studies of nonlinear oscillations in chemical systems. Philosophical Magazine Series 7 2 , 11 , — Fluctuations in the abundance of a species considered mathematically. Nature , , — References [1] Ait-Sahalia, Y. MR m [4] Ludwig Arnold , N. MR 97i , MR m , MR a , MR h , MR 95g [15] D.


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MR g , MR 99d , MR 97h , MR 86d , MR j , MR d , MR f , MR e , Rand , Phase portraits and bifurcations of the nonlinear oscillator: , Internat. Kloeden , Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients , Proc. MR c , MR f [46] P. MR e [47] Peter E. MR 94b [48] Kruse, R. MR 92m , Conference paper.

Markov Chain Monte Carlo and the Metropolis Alogorithm

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Arfken, G. Google Scholar. Cai, G.

Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear

CrossRef Google Scholar. WeC1—06, Kyoto, Japan. Dimentberg, M. Gradshteyn, I. Gurley, K.

Analysis & Probability

Kontorovich, V. Li, Q. Liu, B. Nakayama, J. Shinozuka, M. Sondhi, M. MathSciNet Google Scholar.