Abstract
The explicit form of the transition density is determined for the solution ξ(t) of the stochastic diffusion equation dξ(t)=a(ξ(t))dt+dw(t), where a(z)=α for x ε [a, b] and a(x)=0 for x ∉ [a, b], w(t) is a Wiener process.
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H. Bateman and A. Erdelyi, Tables of Integral Transforms [Russian translation], Vol. 1, Nauka, Moscow (1969).
A. D. Borisenko and T. N. Rylova, “Finding the distribution of particle diffusion in a two-layer medium on a plane,” Vychisl. Prikl. Mat., No. 42, 97–103 (1980).
I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1968).
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 99–105, 1987.
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Almazov, M. Explicit expression for the transition density of the solution of a stochastic diffusion equation with piecewise-constant drift coefficient. J Math Sci 63, 484–489 (1993). https://doi.org/10.1007/BF01849536
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DOI: https://doi.org/10.1007/BF01849536