On the Rate at Which a Homogeneous Diffusion Approaches a Limit, an Application of Large Deviation Theory to Certain Stochastic Integrals
Stroock, Daniel W.
Ann. Probab., Tome 14 (1986) no. 4, p. 840-859 / Harvested from Project Euclid
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Let $X(T)$ be the solution to a stochastic differential equation whose coefficients are homogeneous of degree 1 (e.g., a linear S.D.E.). Under mild conditions, it is shown that limits like $\lim_{T\rightarrow\infty} \frac{1}{T} \log P(|X(T)|/|X(0)| \geq R)$ exist and a formula is provided for their computation. The techniques developed apply to a broad class of situations besides the one treated here.
Publié le : 1986-07-14
Classification:  Diffusion,  large deviations,  60J60,  60F10,  60H05 
@article{1176992441,
     author = {Stroock, Daniel W.},
     title = {On the Rate at Which a Homogeneous Diffusion Approaches a Limit, an Application of Large Deviation Theory to Certain Stochastic Integrals},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 840-859},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992441}
}

Stroock, Daniel W. On the Rate at Which a Homogeneous Diffusion Approaches a Limit, an Application of Large Deviation Theory to Certain Stochastic Integrals. Ann. Probab., Tome 14 (1986) no. 4, pp.  840-859. http://gdmltest.u-ga.fr/item/1176992441/