TY - JOUR
T1 - Pathwise estimates for an effective dynamics
AU - Legoll, Frédéric
AU - Lelièvre, Tony
AU - Olla, Stefano
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - Starting from the overdamped Langevin dynamics in Rn, dXt=−∇V(Xt)dt+2β−1dWt we consider a scalar Markov process ξt which approximates the dynamics of the first component Xt1. In the previous work (Legoll and Lelièvre, 2010), the fact that (ξt)t≥0 is a good approximation of (Xt1)t≥0 is proven in terms of time marginals, under assumptions quantifying the timescale separation between the first component and the other components of Xt. Here, we prove an upper bound on the trajectorial error E(sup0≤t≤T|Xt1−ξt|) for any T>0, under a similar set of assumptions. We also show that the technique of proof can be used to obtain quantitative averaging results.
AB - Starting from the overdamped Langevin dynamics in Rn, dXt=−∇V(Xt)dt+2β−1dWt we consider a scalar Markov process ξt which approximates the dynamics of the first component Xt1. In the previous work (Legoll and Lelièvre, 2010), the fact that (ξt)t≥0 is a good approximation of (Xt1)t≥0 is proven in terms of time marginals, under assumptions quantifying the timescale separation between the first component and the other components of Xt. Here, we prove an upper bound on the trajectorial error E(sup0≤t≤T|Xt1−ξt|) for any T>0, under a similar set of assumptions. We also show that the technique of proof can be used to obtain quantitative averaging results.
KW - Averaging
KW - Effective dynamics for SDEs
KW - Pathwise estimates
UR - https://www.scopus.com/pages/publications/85011311764
U2 - 10.1016/j.spa.2017.01.001
DO - 10.1016/j.spa.2017.01.001
M3 - Article
AN - SCOPUS:85011311764
SN - 0304-4149
VL - 127
SP - 2841
EP - 2863
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 9
ER -