Electronic Journal of Probability

Concentration inequalities for Stochastic Differential Equations with additive fractional noise

Maylis Varvenne

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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

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

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

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Digital Object Identifier

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

concentration inequalities fractional Brownian motion occupation measures Stochastic Differential Equations

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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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