The series expansion for the solution of the integral equation for the first-passagetime probability density function, obtained by resorting to the fixed point theorem, is used to achieve approximate evaluations for which error bounds are indicated. A different use of the fixed point theorem is then made to determine lower and upper bounds for asymptotic approximations, and to examine their range of validity.
On the evaluation and asymptotic approximations for first-passage-time probabilities
SACERDOTE, Laura Lea;
1996-01-01
Abstract
The series expansion for the solution of the integral equation for the first-passagetime probability density function, obtained by resorting to the fixed point theorem, is used to achieve approximate evaluations for which error bounds are indicated. A different use of the fixed point theorem is then made to determine lower and upper bounds for asymptotic approximations, and to examine their range of validity.
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