On Durbin's Series for the Density of First Passage Times
| Autor: | Paul Zipkin |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Statistics and Probability
Pointwise convergence Series (mathematics) 65N21 General Mathematics Mathematical analysis Boundary (topology) First passage time Integral equation Wiener process symbols.namesake 58J35 Iterated function symbols 60J65 Statistics Probability and Uncertainty First-hitting-time model Convergent series Mathematics |
| Zdroj: | J. Appl. Probab. 48, no. 3 (2011), 713-722 |
| ISSN: | 1475-6072 0021-9002 |
| DOI: | 10.1239/jap/1316796909 |
| Popis: | Durbin (1992) derived a convergent series for the density of the first passage time of a Weiner process to a curved boundary. We show that the successive partial sums of this series can be expressed as the iterates of the standard substitution method for solving an integral equation. The calculation is thus simpler than it first appears. We also show that, under a certain condition, the series converges uniformly. This strengthens Durbin's result of pointwise convergence. Finally, we present a modified procedure, based on scaling, which sometimes works better. These approaches cover some cases that Durbin did not. |
| Databáze: | OpenAIRE |
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