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

Open Mathematics (2003)

- Volume: 1, Issue: 1, page 86-96
- ISSN: 2391-5455

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topVitalii Gasanenko. "On asymptotic independence of the exit moment and position from a small domain for diffusion processes." Open Mathematics 1.1 (2003): 86-96. <http://eudml.org/doc/268812>.

@article{VitaliiGasanenko2003,

abstract = {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 \[Eexp( - \lambda T\_\varepsilon )f(\frac\{\{\xi (T\_\varepsilon )\}\}\{\varepsilon \}) - Eexp( - \lambda T\_\varepsilon )Ef(\frac\{\{\xi (T\_\varepsilon )\}\}\{\varepsilon \}),\varepsilon \searrow 0,\lambda > 0.\]},

author = {Vitalii Gasanenko},

journal = {Open Mathematics},

keywords = {60 J 50},

language = {eng},

number = {1},

pages = {86-96},

title = {On asymptotic independence of the exit moment and position from a small domain for diffusion processes},

url = {http://eudml.org/doc/268812},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Vitalii Gasanenko

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

JO - Open Mathematics

PY - 2003

VL - 1

IS - 1

SP - 86

EP - 96

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

LA - eng

KW - 60 J 50

UR - http://eudml.org/doc/268812

ER -

## References

top- [1] M. Liao, Hitting distributions of small geodesic spheres, Ann. Probab., 16 (1988), 1039–1050 Zbl0651.58037
- [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) Zbl0429.60002

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