dc.contributor.author | Harang, Fabian | |
dc.contributor.author | Nilssen, Torstein | |
dc.contributor.author | Proske, Frank Norbert | |
dc.date.accessioned | 2023-08-16T09:18:47Z | |
dc.date.available | 2023-08-16T09:18:47Z | |
dc.date.created | 2021-12-31T13:47:28Z | |
dc.date.issued | 2022 | |
dc.identifier.issn | 1744-2508 | |
dc.identifier.uri | https://hdl.handle.net/11250/3084358 | |
dc.description.abstract | In this article, we will present a new perspective on the variable-order fractional calculus, which allows for differentiation and integration to a variable order. The concept of multifractional calculus has been a scarcely studied topic within the field of functional analysis in the past 20 years. We develop a multifractional differential operator which acts as the inverse of the multifractional integral operator. This is done by solving the Abel integral equation generalized to a multifractional order. With this new multifractional differential operator, we prove a Girsanov's theorem for multifractional Brownian motions of Riemann–Liouville type. As an application, we show how Girsanov's theorem can then be applied to prove the existence of a unique strong solution to stochastic differential equations where the drift coefficient is merely of linear growth, and the driving noise is given by a non-stationary multifractional Brownian motion with a Hurst parameter as a function of time. The Hurst functions we study will take values in a bounded subset of (0,1/2) . The application of multifractional calculus to SDEs is based on a generalization of the works of D. Nualart and Y. Ouknine [Regularization of differential equations by fractional noise, Stoch Process Appl. 102(1) (2002), pp. 103–116]. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Taylor and Francis | en_US |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/deed.no | * |
dc.title | GIRSANOV THEOREM FOR MULTIFRACTIONAL BROWNIAN PROCESSES | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | submittedVersion | en_US |
dc.source.pagenumber | 1137-1165 | en_US |
dc.source.volume | 94 | en_US |
dc.source.journal | Stochastics: An International Journal of Probability and Stochastic Processes | en_US |
dc.source.issue | 8 | en_US |
dc.identifier.doi | 10.1080/17442508.2022.2027948 | |
dc.identifier.cristin | 1973153 | |
cristin.ispublished | true | |
cristin.fulltext | preprint | |
cristin.qualitycode | 1 | |