Multilevel Monte Carlo method for ergodic SDEs without contractivity
作者： Wei Fang , Michael B. Giles
DOI: 10.1016/J.JMAA.2018.12.032
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摘要: Abstract This paper proposes a new multilevel Monte Carlo (MLMC) method for the ergodic SDEs which do not satisfy contractivity condition. By introducing change of measure technique, we simulate path with and add Radon–Nikodym derivative to estimator. We can show strong error is uniformly bounded respect T. Moreover, variance level estimators increase linearly in T, great reduction compared exponential standard MLMC. Then total computational cost reduced O ( e − 2 | log ) from 3 method. Numerical experiments support our analysis.
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sci-hub.se 参考文章(30)
Yuan Xia, Michael B. Giles, Multilevel Path Simulation for Jump-Diffusion SDEs Springer, Berlin, Heidelberg. pp. 695- 708 ,(2012) , 10.1007/978-3-642-27440-4_41
Christian Soize, The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions ,(1994)
Xuerong Mao, Stochastic Differential Equations and Applications ,(2008)
Peter E Kloeden, Eckhard Platen, Matthias Gelbrich, Werner Romisch, Numerical Solution of Stochastic Differential Equations ,(1992)
S. Juneja, P. Shahabuddin, Chapter 11 Rare-Event Simulation Techniques: An Introduction and Recent Advances Simulation. ,vol. 13, pp. 291- 350 ,(2006) , 10.1016/S0927-0507(06)13011-X
Michael V. Tretyakov, Grigori Milstein, Grigori Noah Milstein, Stochastic Numerics for Mathematical Physics ,(2004)
Riccardo Gasparotto, Optimised Importance Sampling in Multilevel Monte Carlo ,(2015)
Desmond J. Higham, Xuerong Mao, Andrew M. Stuart, Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations SIAM Journal on Numerical Analysis. ,vol. 40, pp. 1041- 1063 ,(2002) , 10.1137/S0036142901389530
Gareth O. Roberts, Richard L. Tweedie, Exponential convergence of Langevin distributions and their discrete approximations Bernoulli. ,vol. 2, pp. 341- 363 ,(1996) , 10.2307/3318418
Niels Richard Hansen, Geometric ergodicity of discrete-time approximations to multivariate diffusions Bernoulli. ,vol. 9, pp. 725- 743 ,(2003) , 10.3150/BJ/1066223276