On accuracy of approximations for wiener probabilities to stay between square root boundaries Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
||
|---|---|---|---|
| Output data | Year: 2025, Volume: 22, Number: 2, Pages: 1614-1625 Pages count : 12 DOI: 10.33048/semi.2025.22.098 | ||
| Tags | Brownian motion, Wiener process, square root boundaries, exit time, accuracy of approximation | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia | FWNF-2022-0010 |
Abstract:
Several asymptotic formulas for probabilities of the Wiener process to stay between different square root boundaries are known after papers of Breiman (1965), Sato (1977), Novikov (1979, 1981), Gartner (1982), Uchiyama (1980), Greenwood and Perkins (1983). In the present work we investigate accuracy of these approximations. We present several general estimates which contain the ones obtained earlier by Uchiyama in the limiting case of one boundary.
Cite:
Sakhanenko A.I.
On accuracy of approximations for wiener probabilities to stay between square root boundaries
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.1614-1625. DOI: 10.33048/semi.2025.22.098 WOS Scopus
On accuracy of approximations for wiener probabilities to stay between square root boundaries
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.1614-1625. DOI: 10.33048/semi.2025.22.098 WOS Scopus
Dates:
| Accepted: | Oct 14, 2025 |
| Published print: | Dec 29, 2025 |
| Published online: | Dec 29, 2025 |
Identifiers:
| ≡ Web of science: | WOS:001835172000040 |
| ≡ Scopus: | 2-s2.0-105026511288 |