Moment estimates for solutions of linear stochastic differential
equations driven by analytic fractional Brownian motion
Jeremie M Unterberger, Institut Elie Cartan de Nancy - Universite Henri Poincare - Nancy (France)
Abstract
As a general rule, differential equations driven by a multi-dimensional irregular path Γ are
solved by constructing a rough path over Γ. The domain of definition -- and also
estimates -- of the solutions depend on upper bounds for the rough path; these
general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic
differential equations with linear coefficients
driven by a Gaussian process with H"older regularity α<1/2.
We prove here (by showing convergence of Chen's series)
that linear stochastic differential equations driven by analytic fractional Brownian motion [6,7]
with arbitrary Hurst index α∈(0,1) may be solved on the closed upper half-plane, and that the solutions have finite variance
Full text: PDF
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona.
The preferred way is to send a scanned (jpeg or pdf) copy of the signed copyright form to the managing editor Philippe Carmona at ejpecpme@math.univ-nantes.fr.
If a paper has several authors, the corresponding author signs the copyright form
on behalf of all the authors.