Minoration en temps petit de la densité d’une diffusion dégénérée. (Lower estimate for small times of the density of a degenerate diffusion). (French) Zbl 0637.58034

Let the diffusion on R d be given by the Stratonovich stochastic differential equation \(dx_ t=\sum X_ i(x_ t)dw_ i\), the Lie algebra of vector fields \(X_ i\) at each point is equal to R d. The author proves that the density \(p_ t(x,y)\) of \(x_ t\) satisfies the inequality \[ \underline{\lim}_{t\to 0}2t \log P_ t(x,y)\geq -d^ 2(x,y) \] where d denotes a semi-Riemannian metric associated to the generator of diffusion.
Reviewer: S.Eloshvili


58J65 Diffusion processes and stochastic analysis on manifolds
60G60 Random fields
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