Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion

Saussereau, Bruno

doi:10.3150/10-bej324

Cited by 49 publications

(34 citation statements)

References 34 publications

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“…For studying the equation (0.2) in full generality, one needs further ingredients, and we will use Lyon's rough paths theory to achieve this goal. Let us mention that our results imply those obtained in [Sau12] in case of fBm. There is a further challenge when studying transportation-cost inequalities for solutions to (0.2) for general Gaussian processes X.…”

Section: Introductionsupporting

confidence: 89%

Transportation–cost inequalities for diffusions driven by Gaussian processes

Riedel¹

2017

Electron. J. Probab.

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We prove transportation-cost inequalities for the law of SDE solutions driven by general Gaussian processes. Examples include the fractional Brownian motion, but also more general processes like bifractional Brownian motion. In case of multiplicative noise, our main tool is Lyons' rough paths theory. We also give a new proof of Talagrand's transportation-cost inequality on Gaussian Fréchet spaces. We finally show that establishing transportation-cost inequalities implies that there is an easy criterion for proving Gaussian tail estimates for functions defined on that space. This result can be seen as a further generalization of the "generalized Fernique theorem" on Gaussian spaces [FH14, Theorem 11.7] used in rough paths theory.If (0.1) holds, we will say that T p (C) holds for the measure µ.

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Section: Introductionsupporting

confidence: 89%

Transportation–cost inequalities for diffusions driven by Gaussian processes

Riedel¹

2017

Electron. J. Probab.

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“…) and there exist constants α, L > 0 such that: ⊲ This contractivity assumption on the drift term is quite usual to get long-time concentration results (see [4,14] for instance). At this stage, a more general framework seems elusive.…”

Section: Assumptions and General Resultsmentioning

confidence: 99%

“…However, his results do not give long-time concentration, which is our focus here. In the setting of fractional noise, T.Guendouzi [7] and B.Saussereau [14] have studied transportation inequalities with different metrics in the case where H ∈ (1/2, 1). In particular, B.Saussereau gave an important contribution: he proved T 1 (C) and T 2 (C) for the law of (Y t ) t∈ [0,T ] in various settings and he got a result of large-time asymptotics in the case of a contractive drift.…”

Section: Introductionmentioning

confidence: 99%

Concentration inequalities for Stochastic Differential Equations with additive fractional noise

Varvenne¹

2019

Electron. J. Probab.

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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 ∈ (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.

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“…both the uniform and the L 2 distances on the path space for the segment process associated to a class of neutral function stochastic differential equations. B. Saussereau [23] studied the T 2 pCq for SDE driven by a fractional Brownian motion, and S. Riedel [22] extended this result to the law of SDE driven by general Gaussian processes by using Lyons' rough paths theory. S. Pal [21] proved that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, satisfy quadratic transportation cost inequality under the uniform metric.…”

Section: Introductionmentioning

confidence: 99%