A Limit Theorem for Stochastic Acceleration
نویسندگان
چکیده
We consider the motion of a particle in a weak mean zero random force field F, which depends on the position, x(t), and the velocity, v(t) = 2(0. The equation of motion is 2(0 = ef(x( t ) , v(t), 0~), where x( ') and v(-) take values in R d, d > 3, and co ranges over some probability space. We show, under suitable mixing and moment conditions on F, that as e--+ 0, v~( t ) v(t/e 2) converges weakly to a diffusion Markov process v(t), and e2x~(t) converges weakly to S v(s)ds + x, where x = lim e2x~(0). 0
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تاریخ انتشار 1980