A Note on the Smoluchowski-kramers Approximation for the Langevin Equation with Reflection∗
نویسنده
چکیده
According to the Smoluchowski-Kramers approximation, the solution of the equation μq̈ t = b(q μ t ) − q̇ t + Σ(q t )Ẇt, q 0 = q, q̇ 0 = p converges to the solution of the equation q̇t = b(qt) + Σ(qt)Ẇt, q0 = q as μ → 0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.
منابع مشابه
ASYMPTOTIC PROBLEMS FOR STOCHASTIC PROCESSES WITH REFLECTION AND RELATED PDE ’ s Konstantinos Spiliopoulos , Doctor of Philosophy , 2009
Title of dissertation: ASYMPTOTIC PROBLEMS FOR STOCHASTIC PROCESSES WITH REFLECTION AND RELATED PDE’s Konstantinos Spiliopoulos, Doctor of Philosophy, 2009 Dissertation directed by: Professor Mark I. Freidlin Department of Mathematics Asymptotic problems for stochastic processes with reflection and for related partial differential equations (PDE’s) are considered in this thesis. The stochastic ...
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