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doi:10.22028/D291-36246 | Title: | Itô’s formula for Gaussian processes with stochastic discontinuities |
| Author(s): | Bender, Christian |
| Language: | English |
| Title: | The annals of probability |
| Volume: | 48 |
| Issue: | 1 |
| Startpage: | 458 |
| Endpage: | 492 |
| Publisher/Platform: | Institute of Mathematical Statistics |
| Year of Publication: | 2020 |
| Free key words: | Gaussian processes Itô’s formula stochastic discontinuities stochastic integrals S-transform |
| DDC notations: | 510 Mathematics |
| Publikation type: | Journal Article |
| Abstract: | We introduce a Skorokhod type integral and prove an Itô formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Itô formula unifies and extends the classical one for general (i.e., possibly discontinuous) Gaussian martingales in the sense of Itô integration and the one for stochastically continuous Gaussian non-martingales in the Skorokhod sense, which was first derived in Alòs et al. (Ann. Probab. 29 (2001) 766–801). |
| DOI of the first publication: | 10.1214/19-AOP1369 |
| URL of the first publication: | https://projecteuclid.org/journals/annals-of-probability/volume-48/issue-1/It%c3%b4s-formula-for-Gaussian-processes-with-stochastic-discontinuities/10.1214/19-AOP1369.short |
| Link to this record: | urn:nbn:de:bsz:291--ds-362463 hdl:20.500.11880/33121 http://dx.doi.org/10.22028/D291-36246 |
| ISSN: | 0091-1798 |
| Date of registration: | 15-Jun-2022 |
| Faculty: | MI - Fakultät für Mathematik und Informatik |
| Department: | MI - Mathematik |
| Professorship: | MI - Prof. Dr. Christian Bender |
| Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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