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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.