摘要
For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.
For a given probability density function ρ(x) on Rd,we construct a(non-stationary) diffusion process xt,starting at any point x in Rd,such that 1/T∫T0 δ(xt-x)dt converges to ρ(x) almost surely.The rate of this convergence is also investigated.To find this rate,we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.
基金
supported by the Simons Foundation (Grant No. 209206)
a General Research Fund of the University of Kansas
