Concentration inequalities for Stochastic Differential Equations with additive fractional noise

Maylis Varvenne (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 ∈ (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.

Mots clés: Concentration inequalities; Fractional Brownian Motion; Occupation measures; Stochastic Differential Equations

Domaines: Probabilités [math.PR]

Maylis Varvenne. Concentration inequalities for Stochastic Differential Equations with additive fractional noise. Electronic Journal of Probability, In press. ⟨hal-01975471v3⟩