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SUMMARY:Ergodic Stochastic Differential Equations and Sampling: A numerica
 l analysis perspective - Kostas Zygalakis\, University of Edinburgh
DTSTART:20181206T150000Z
DTEND:20181206T160000Z
UID:TALK112375@talks.cam.ac.uk
CONTACT:Matthew Thorpe
DESCRIPTION:Understanding the long time behaviour of solutions to ergodic 
 stochastic differential equations is an important question with relevance 
 in many field of applied mathematics and statistics. Hence\, designing app
 ropriate numerical algorithms that are able to capture such behaviour corr
 ectly is extremely important. A recently introduced framework [1\,2\,3] us
 ing backward error analysis allows us to characterise the bias with which 
 one approximates the invariant measure (in the absence of the accept/rejec
 t correction). These ideas will be used to design numerical methods exploi
 ting the variance reduction of recently introduced nonreversible Langevin 
 samplers [4\,5]. Finally if there is time we will discuss\, how things ide
 as can be combined with the idea of Multilevel Monte Carlo [6] to produce 
 unbiased estimates of ergodic averages without the need the of an accept-r
 eject correction [7] and optimal computational cost.\n\n\n\n[1] K.C. Zygal
 akis. On the existence and applications of modified equations for stochast
 ic differential equations. SIAM J. Sci. Comput.\, 33:102-130\, 2011.\n[2] 
 A. Abdulle\, G. Vilmart\, and K. C. Zygalakis. High order numerical approx
 imation of the invariant measure of ergodic sdes. SIAM J. Numer. Anal.\, 5
 2(4):1600-1622\, 2014.\n[3] A. Abdulle\, G. Vilmart\, and K.C. Zygalakis\,
  Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics
 . SIAM J. Numer. Anal.\, 53(1):1-16\, 2015.\n[4] A. Duncan\, G. A. Pavliot
 is and T. Lelievre\, Variance Reduction using Nonreversible Langevin Sampl
 ers\, J. Stat. Phys.\, 163(3):457-491\, 2016.\n[5] A. Duncan\, G. A. Pavli
 otis and K. C. Zygalakis\, Nonreversible Langevin Samplers: Splitting Sche
 mes\, Analysis and Implementation\, arXiv:1701.04247\n[6]  M.B. Giles\, Mu
 tlilevel Monte Carlo methods\, Acta Numerica\, 24:259-328\, 2015.\n[7] L. 
 Szpruch\, S. Vollmer\, K. C. Zygalakis and M. B. Giles\, Multi Level Monte
  Carlo methods for a class of ergodic stochastic differential equations. a
 rXiv:1605.01384.
LOCATION:MR 14
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