Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions

DOI10.1214/12-AIHP522zbMath1286.60051arXiv1104.3884WikidataQ126120478 ScholiaQ126120478MaRDI QIDQ2438257

Cheng Ouyang, Samy Tindel, Fabrice Baudoin

Publication date: 10 March 2014

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.3884

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (20)

Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions ⋮ On probability laws of solutions to differential systems driven by a fractional Brownian motion ⋮ Bismut type derivative formulae and gradient estimate for multiplicative SDEs with fractional noises ⋮ Smooth density for some nilpotent rough differential equations ⋮ Density bounds for solutions to differential equations driven by Gaussian rough paths ⋮ Existence and upper bound for the density of solutions of stochastic differential equations driven by generalized grey noise ⋮ Sensitivity of rough differential equations: an approach through the omega lemma ⋮ Logarithmic Sobolev inequalities for fractional diffusion ⋮ On inference for fractional differential equations ⋮ On the (non)stationary density of fractional-driven stochastic differential equations ⋮ On the lack of Gaussian tail for rough line integrals along fractional Brownian paths ⋮ Smooth density for the solution of scalar SDEs with locally Lipschitz coefficients under Hörmander condition ⋮ Nourdin-Peccati analysis on Wiener and Wiener-Poisson space for general distributions ⋮ Smoothness of the density for solutions to Gaussian rough differential equations ⋮ Density of the signature process of fBm ⋮ Density estimates and central limit theorem for the functional of fractional SDEs ⋮ Varadhan estimates for rough differential equations driven by fractional Brownian motions ⋮ Derivative formulas and applications for degenerate stochastic differential equations with fractional noises ⋮ Integration by Parts Formula and Applications for SDEs Driven by Fractional Brownian Motions ⋮ Bismut formulas and applications for stochastic (functional) differential equations driven by fractional Brownian motions

Cites Work

• Unnamed Item
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• Unnamed Item
• Integrability and tail estimates for Gaussian rough differential equations
• A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion
• Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion
• Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions
• Trees and asymptotic expansions for fractional stochastic differential equations
• Operators associated with a stochastic differential equation driven by fractional Brownian motions
• Densities for rough differential equations under Hörmander's condition
• Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion
• Integration with respect to fractal functions and stochastic calculus. I
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• Differential equations driven by fractional Brownian motion
• Ergodicity of stochastic differential equations driven by fractional Brownian motion
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Potential theory for hyperbolic SPDEs.
• Controlling rough paths
• On inference for fractional differential equations
• Discretizing the fractional Lévy area
• Rough evolution equations
• Ergodic theory for SDEs with extrinsic memory
• Large deviations for rough paths of the fractional Brownian motion
• A version of Hörmander's theorem for the fractional Brownian motion
• ESTIMATES FOR THE SOLUTION TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H ∈ (⅓, ½)
• The Malliavin Calculus and Related Topics
• Multidimensional Stochastic Processes as Rough Paths
• Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation
• Non-degeneracy of Wiener functionals arising from rough differential equations
• System Control and Rough Paths

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