Stochastic differential equations driven by stable processes for which pathwise uniqueness fails
| dc.contributor.author | Burdzy, Krzysztof | |
| dc.contributor.author | Bass, Richard F. | |
| dc.contributor.author | Chen, Zhen-Qing | |
| dc.date.accessioned | 2005-12-01 | |
| dc.date.available | 2005-12-01 | |
| dc.date.issued | 2004-05 | |
| dc.description.abstract | Let Z [subscript] t be a one-dimensional symmetric stable process of order [alpha] with [alpha is an element of the set] (0, 2) and consider the stochastic differential equation dX [subscript] t = [omega] (X [subscript] t−)dZ [subscript]t. For [beta] < 1 [divided by alpha] ^ 1, we show there exists a function that is bounded above and below by positive constants and which is Holder continuous of order [beta] but for which pathwise uniqueness of the stochastic differential equation does not hold. This result is sharp. | en |
| dc.description.sponsorship | Research partially supported by NSF grants DMS-9988496 and DMS-0071486. | en |
| dc.format.extent | 179719 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | Bass, R.F., K. Burdzy, & Z.Q. Chen. (2004). Stochastic differential equations driven by stable processes for which pathwise uniqueness fails. Stochastic Processes and Their Applications, 111(1), 1-15. | en |
| dc.identifier.uri | http://hdl.handle.net/1773/2228 | |
| dc.language.iso | en_US | |
| dc.publisher | North-Holland (Elsevier) | en |
| dc.subject | Stable processes | en |
| dc.subject | pathwise uniqueness | en |
| dc.subject | stochastic differential equations | en |
| dc.subject | time change | en |
| dc.subject | crossing estimates | en |
| dc.title | Stochastic differential equations driven by stable processes for which pathwise uniqueness fails | en |
| dc.title.alternative | SDEs driven by stable processes | en |
| dc.type | Article | en |