Geodesic
Strangely sweeping one-dimensional diffusion
Annales Polonici Mathematici, Tome 58 (1993) no. 1, pp. 37-45
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Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = Prob{X(t) ≥ 0} as t → ∞ and construct an equation such that $lim sup_{t→∞} t^{-1} ∫_0^t p(s) ds = 1$ and $lim inf_{t→∞}t^{-1} ∫_0^t p(s) ds = 0$.
DOI : 10.4064/ap-58-1-37-45
Keywords: diffusion process, parabolic equation 
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Ryszard Rudnicki. Strangely sweeping one-dimensional diffusion. Annales Polonici Mathematici, Tome 58 (1993) no. 1, pp. 37-45. doi: 10.4064/ap-58-1-37-45

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