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

• Autorzy: Vitalii Gasanenko
• Języki publikacji: EN

Abstrakty

EN

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 $$Eexp( - \lambda T_\varepsilon )f(\frac{{\xi (T_\varepsilon )}}{\varepsilon }) - Eexp( - \lambda T_\varepsilon )Ef(\frac{{\xi (T_\varepsilon )}}{\varepsilon }),\varepsilon \searrow 0,\lambda > 0.$$

Słowa kluczowe

EN

Diffusion process; exit moment and exit place; elliptic boundary problems; 60 J 50

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 1
• Strony: 86-96

Daty

wydano

2003-03-01

online

2003-03-01

Twórcy

autor

Vitalii Gasanenko

• National Academy of Science of Ukraine

Bibliografia

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

Identyfikatory

DOI

10.2478/BF02475666