A probabilistic solution to the Stroock–Williams equation
نویسندگان
چکیده
منابع مشابه
A Probabilistic Solution to the Stroock-Williams Equation
We consider the initial boundary value problem u t = µu x + 1 2 u xx (t > 0, x ≥ 0) u(0, x) = f (x) (x ≥ 0) u t (t, 0) = ν u x (t, 0) (t > 0) of Stroock and Williams [12] where µ, ν ∈ IR and the boundary condition is not of Feller's type when ν < 0. We show that when f belongs to C 1 b with f (∞) = 0 then the following probabilistic representation of the solution is valid u(t, x) = E x f (X t) ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2014
ISSN: 0091-1798
DOI: 10.1214/13-aop865