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

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Gasanenko V.

Open Mathematics

2003

tom 1

nr 1

86-96

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

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1 Open Mathematics

1 Gasanenko V.

1 2003

Wyniki wyszukiwania

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