On asymptotic independence of the exit moment and position from a small domain for diffusion processes

Vitalii Gasanenko

Open Mathematics, Tome 1 (2003), p. 86-96 / Harvested from The Polish Digital Mathematics Library

Résumé

If ξ(t) is the solution of homogeneous SDE in R m, and T ∃ is the first exit moment of the process from a small domain D ∃, then the total expansion for the following functional showing independence of the exit time and exit place is $E e x p (- λ T_{ε}) f (\frac{ξ (T_{ε})}{ε}) - E e x p (- λ T_{ε}) E f (\frac{ξ (T_{ε})}{ε}), ε ↘ 0, λ > 0 .$

Publié le : 2003-01-01

Zbl 1030.60072

EUDML-ID : urn:eudml:doc:268812

@article{bwmeta1.element.doi-10_2478_BF02475666,
     author = {Vitalii Gasanenko},
     title = {On asymptotic independence of the exit moment and position from a small domain for diffusion processes},
     journal = {Open Mathematics},
     volume = {1},
     year = {2003},
     pages = {86-96},
     zbl = {1030.60072},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475666}
}

Vitalii Gasanenko. On asymptotic independence of the exit moment and position from a small domain for diffusion processes. Open Mathematics, Tome 1 (2003) pp. 86-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475666/

Bibliographie

[1] M. Liao, Hitting distributions of small geodesic spheres, Ann. Probab., 16 (1988), 1039–1050 | Zbl 0651.58037

[2] V.A. Gasanenko, A total expansion functional of exit time from a small ball for diffusion process, International Journal Istatistik, Vol. 3, Issue 3 (2000), 83–91

[3] O.A. Ladyjenskai and N.N. Ural’ceva, Linear and quasilinear equation of elliptic type, “Nauka”, Moscow (1973)

[4] I.I. Gikhman and A.V. Skorokhod, Introduction in the theory of random, “Nauka”, Moscow (1977) | Zbl 0429.60002