Stochastic calculus for convoluted Lévy processes
| dc.creator | Bender, Christian | |
| dc.creator | Marquardt, Tina | |
| dc.date | 2008-05-14 | |
| dc.date.accessioned | 2026-07-07T12:18:52Z | |
| dc.date.available | 2026-07-07T12:18:52Z | |
| dc.description | We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation Lévy process with a Volterra-type kernel. This class of processes contains, for example, fractional Lévy processes as studied by Marquardt [Bernoulli 12 (2006) 1090--1126.] The integral which we introduce is a Skorokhod integral. Nonetheless, we avoid the technicalities from Malliavin calculus and white noise analysis and give an elementary definition based on expectations under change of measure. As a main result, we derive an Itô formula which separates the different contributions from the memory due to the convolution and from the jumps. | |
| dc.description | Published in at http://dx.doi.org/10.3150/07-BEJ115 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) | |
| dc.identifier | https://arxiv.org/abs/0805.2084 | |
| dc.identifier | http://arxiv.org/abs/0805.2084 | |
| dc.identifier | Bernoulli 2008, Vol. 14, No. 2, 499-518 | |
| dc.identifier | doi:10.3150/07-BEJ115 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212561 | |
| dc.subject | Probability | |
| dc.title | Stochastic calculus for convoluted Lévy processes | |
| dc.type | text |