Profile cut-off phenomenon for the ergodic Feller root process

Gerardo Barrera and Liliana Esquivel

Stochastic Processes and their Applications, 2025, vol. 183, issue C

Abstract: The present manuscript is devoted to the study of the convergence to equilibrium as the noise intensity ɛ>0 tends to zero for ergodic random systems out of equilibrium driven by multiplicative non-linear noise of the type dXtɛ(x)=(b−aXtɛ(x))dt+ɛXtɛ(x)dBt,X0ɛ(x)=x,t⩾0,where x⩾0, a>0 and b>0 are constants, and (Bt)t⩾0 is a one dimensional standard Brownian motion. More precisely, we show the strongest notion of asymptotic profile cut-off phenomenon in the total variation distance and in the renormalized Wasserstein distance when ɛ tends to zero with explicit cut-off time, explicit time window, and explicit profile function. In addition, asymptotics of the so-called mixing times are given explicitly.

Keywords: Affine processes; Asymptotic cut-off phenomenon; Brownian motion; CIR model; Convergence to equilibrium; Decoupling; Fourier transform; Mixing times; Sharp transition; Square-root diffusion; Thermalization; Total variation distance; Wasserstein distance (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104587

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