Predicting the Last Zero of Brownian Motion with Drift
نویسندگان
چکیده
τ∗ = inf { t ∈ [0, T ] | B t ≤ b−(t) or B t ≥ b+(t) } where the function t 7→ b−(t) is continuous and increasing on [0, T ] with b−(T ) = 0 , the function t 7→ b+(t) is continuous and decreasing on [0, T ] with b+(T ) = 0 , and the pair b− and b+ can be characterised as the unique solution to a coupled system of nonlinear Volterra integral equations. This also yields an explicit formula for V∗ in terms of b− and b+ . If μ = 0 then b− = −b+ and there is a closed form expression for b± as shown in [10] using the method of time change from [4]. The latter method cannot be extended to the case when μ 6= 0 and the present paper settles the remaining cases using a different approach.
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تاریخ انتشار 2008