On Reflecting Brownian Motion with Drift
نویسنده
چکیده
Let B = (Bt)t≥0 be a standard Brownian motion started at zero, and let μ ∈ R be a given and fixed constant. Set B t = Bt+μt and S t = max 0≤s≤t B s for t ≥ 0 . Then the process: (x ∨ Sμ)−Bμ = ((x ∨ S t )−B t )t≥0 realises an explicit construction of the reflecting Brownian motion with drift −μ started at x in R+ . Moreover, if the latter process is denoted by Z = (Z t )t≥0 , then the classic Lévy’s theorem extends as follows: ( (x ∨ Sμ)−Bμ, (x ∨ Sμ)− x) law = (Zx, `0(Zx))
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