Stochastic Differential Equations for Sticky Brownian Motion
نویسنده
چکیده
dXt = 12 d` 0 t (X) + I(Xt >0) dBt I(Xt =0) dt = 1 2μ d` 0 t (X) for reflecting Brownian motion X in IR+ sticky at 0 , where X starts at x in the state space, μ ∈ (0,∞) is a given constant, `(X) is the local time of X at 0 , and B is a standard Brownian motion. We prove that both systems (i) have a jointly unique weak solution and (ii) have no strong solution. The latter fact verifies Skorokhod’s conjecture on sticky Brownian motion and provides alternative arguments to those given in the literature.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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