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Sharp bounds for transition probability densities of a class of diffusions

Abstract:
Let pb(x, t, y) be the transition probability density of the one dimensional diffusion process dXt = dWt + b(Xt) dt, where b(.) ∞ ≤ 1. We show that the upper and lower bounds of pb(x, t, y) are achieved for fixed (x, t, y) when b(z) = sgn(y - z) and b(z) = sgn(z -y) respectively. Moreover, the precise bounds are given. © 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

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Journal:
Comptes Rendus Mathematique
Volume:
335
Issue:
11
Pages:
953-957
Publication date:
2002-12-01
DOI:
ISSN:
1631-073X
URN:
uuid:7eca4032-0e1c-49a9-9269-e0835e4eb710
Source identifiers:
147549
Local pid:
pubs:147549
Language:
French

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