ISSN:
1432-0916

Source:
Springer Online Journal Archives 1860-2000

Topics:
Mathematics
,
Physics

Notes:
Abstract We consider the motion of a particle in a weak mean zero random force fieldF, which depends on the position,x(t), and the velocity,v(t)= $$\dot x$$ (t). The equation of motion is $$\ddot x$$ (t)=ɛF(x(t),v(t), ω), wherex(·) andv(·) take values in ℝ d ,d≧3, and ω ranges over some probability space. We show, under suitable mixing and moment conditions onF, that as ɛ→0,v ɛ (t)≡v(t/ɛ2) converges weakly to a diffusion Markov processv(t), and ɛ2 x ɛ (t) converges weakly to $$\int\limits_0^t {v(s)ds + x} $$ , wherex=lim ɛ2 x ɛ (0).

Type of Medium:
Electronic Resource

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