Some Limit Theorems Connected with Brownian Local Time
نویسنده
چکیده
Let B = (Bt)t≥0 be a standard Brownian motion and let (Lt ; t ≥ 0, x ∈R) be a continuous version of its local time process. We show that the following limit limε↓0(1/2ε) ∫ t 0{F(s,Bs− ε)− F(s,Bs + ε)}ds is well defined for a large class of functions F(t,x), and moreover we connect it with the integration with respect to local time Lt . We give an illustrative example of the nonlinearity of the integration with respect to local time in the random case.
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تاریخ انتشار 2006