Electronic Journal of Probability

Concentration inequalities for Stochastic Differential Equations with additive fractional noise

Maylis Varvenne

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Abstract

In this paper, we establish concentration inequalities both for functionals of the whole solution on an interval $[0,T]$ of an additive SDE driven by a fractional Brownian motion with Hurst parameter $H\in (0,1)$ and for functionals of discrete-time observations of this process. Then, we apply this general result to specific functionals related to discrete and continuous-time occupation measures of the process.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 124, 22 pp.

Dates
Received: 15 January 2019
Accepted: 2 November 2019
First available in Project Euclid: 9 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1573268588

Digital Object Identifier
doi:10.1214/19-EJP384

Subjects
Primary: 60G22: Fractional processes, including fractional Brownian motion 60H10: Stochastic ordinary differential equations [See also 34F05] 60E15: Inequalities; stochastic orderings

Keywords
concentration inequalities fractional Brownian motion occupation measures Stochastic Differential Equations

Rights
Creative Commons Attribution 4.0 International License.

Citation

Varvenne, Maylis. Concentration inequalities for Stochastic Differential Equations with additive fractional noise. Electron. J. Probab. 24 (2019), paper no. 124, 22 pp. doi:10.1214/19-EJP384. https://projecteuclid.org/euclid.ejp/1573268588


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