Gaussian estimates for the solutions of some one-dimensional stochastic equations

DOI10.1007/s11118-015-9472-7zbMath1321.60127OpenAlexW2037904233MaRDI QIDQ494710

Nicolas Privault, Tien Dung Nguyen, Giovanni Luca Torrisi

Publication date: 2 September 2015

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://hdl.handle.net/10356/79258

zbMATH Keywords

fractional Brownian motionMalliavin calculusstochastic differential equationsClark-Ocone formulaprobability bounds

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic calculus of variations and the Malliavin calculus (60H07) Random measures (60G57)

Related Items (14)

Tail probabilities of solutions to a generalized Ait-Sahalia interest rate model ⋮ Tail estimates for exponential functionals and applications to SDEs ⋮ Distribution of the integral of maximum processes and applications ⋮ Gaussian density estimates for the solution of singular stochastic Riccati equations. ⋮ Density estimates for solutions of stochastic functional differential equations ⋮ Tail probability estimates for additive functionals ⋮ Density estimates for the solutions of backward stochastic differential equations driven by Gaussian processes ⋮ Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression ⋮ The density of solutions to multifractional stochastic Volterra integro-differential equations ⋮ An integration by parts formula for functionals of the Dirichlet-ferguson measure, and applications ⋮ Density estimates and central limit theorem for the functional of fractional SDEs ⋮ Existence and Besov regularity of the density for a class of SDEs with Volterra noise ⋮ Gaussian lower bounds for the density via Malliavin calculus ⋮ Hurst index estimation in stochastic differential equations driven by fractional Brownian motion

Cites Work

• Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions
• Probability approximation by Clark-Ocone covariance representation
• A Malliavin calculus method to study densities of additive functionals of SDE's with irregular drifts
• Stochastic analysis in discrete and continuous settings. With normal martingales.
• Stein's method on Wiener chaos
• Density formula and concentration inequalities with Malliavin calculus
• Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations
• A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
• Integration with respect to fractal functions and stochastic calculus. I
• Concentration and deviation inequalities in infinite dimensions via covariance representations
• Density estimates for solutions to one dimensional backward SDE's
• Estimates for the density of functionals of SDEs with irregular drift
• OPTIMAL GAUSSIAN DENSITY ESTIMATES FOR A CLASS OF STOCHASTIC EQUATIONS WITH ADDITIVE NOISE
• The Malliavin Calculus and Related Topics
• Equations différentielles stochastiques dans avec conditions aux bords
• The Research Program of Stochastic Deformation (with a View Toward Geometric Mechanics)

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