Brownian Motion with Singular Drift by Richard
نویسندگان
چکیده
dXt = dWt + dAt , where Wt is d-dimensional Brownian motion with d ≥ 2 and the ith component of At is a process of bounded variation that stands in the same relationship to a measure πi as ∫ t 0 f (Xs)ds does to the measure f (x)dx. We prove weak existence and uniqueness for the above stochastic differential equation when the measures πi are members of the Kato class Kd−1. As a typical example, we obtain a Brownian motion that has upward drift when in certain fractal-like sets and show that such a process is unique in law.
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تاریخ انتشار 2003