Law equivalence of Ornstein–Uhlenbeck processes driven by a Lévy process

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00507987" target="_blank" >RIV/67985840:_____/19:00507987 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.indag.2019.05.003" target="_blank" >http://dx.doi.org/10.1016/j.indag.2019.05.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.indag.2019.05.003" target="_blank" >10.1016/j.indag.2019.05.003</a>

Result language
angličtina
Original language name
Law equivalence of Ornstein–Uhlenbeck processes driven by a Lévy process
Original language description
We demonstrate that two Ornstein–Uhlenbeck processes, that is, solutions to certain stochastic differential equations that are driven by a Lévy process L have equivalent laws as long as the eigenvalues of the covariance operator associated to the Wiener part of L are strictly positive. Moreover, we show that in the case where the underlying Lévy process is a purely jump process, which means that neither it has a Wiener part nor the drift, the absolute continuity of the law of one solution with respect to another forces equality of the solutions almost surely.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ19-07129Y" target="_blank" >GJ19-07129Y: Linear-analysis techniques in operator algebras and vice versa</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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