Integration with respect to the non-commutative fractional Brownian motion
| Autor: | Aurélien Deya, René Schott |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Department of Networks, Systems and Services (LORIA - NSS), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
non-commutative stochastic calculus
Statistics and Probability Pure mathematics Fractional Brownian motion 010102 general mathematics [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA] Mathematics - Operator Algebras 01 natural sciences Hurst index [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability Mathematics::Probability integration theory non-commutative fractional Brownian motion Point (geometry) 0101 mathematics Commutative property Mathematics - Probability Mathematics |
| Zdroj: | Bernoulli Bernoulli, 2019, 25 (3), pp.2137-2162. ⟨10.3150/18-BEJ1048⟩ Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2019, 25 (3), pp.2137-2162. ⟨10.3150/18-BEJ1048⟩ Bernoulli 25, no. 3 (2019), 2137-2162 |
| ISSN: | 1350-7265 |
| DOI: | 10.3150/18-BEJ1048⟩ |
| Popis: | International audience; We study the issue of integration with respect to the non-commutative fractional Brownian motion, that is the analog of the standard fractional Brownian in a non-commutative probability setting.When the Hurst index $H$ of the process is stricly larger than $1/2$, integration can be handled through the so-called Young procedure. The situation where $H=1/2$ corresponds to the specific free case, for which an It{\^o}-type approach is known to be possible.When $H |
| Databáze: | OpenAIRE |
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