Stochastic formulations of the parametrix method

DOI10.1051/ps/2018013zbMath1403.60047OpenAlexW2887082605MaRDI QIDQ4615435

Go Yuki, Arturo Kohatsu-Higa

Publication date: 28 January 2019

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/ps/2018013

zbMATH Keywords

stochastic differential equationdensity functionparametrix methodsingular driftGaussian two-sided bounds

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60)

Related Items

Probability density function of SDEs with unbounded and path-dependent drift coefficient, On stochastic Langevin and Fokker-Planck equations: the two-dimensional case, On the relation between the Girsanov transform and the Kolmogorov equations for SPDEs

Cites Work

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• Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift
• A Malliavin calculus method to study densities of additive functionals of SDE's with irregular drifts
• Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions
• Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation
• Hölder continuity property of the densities of SDEs with singular drift coefficients
• A probabilistic interpretation of the parametrix method
• Strong uniqueness for stochastic evolution equations with unbounded measurable drift term
• Comparison theorem and estimates for transition probability densities of diffusion processes
• A simple method for the existence of a density for stochastic evolutions with rough coefficients
• Singular stochastic differential equations.
• Strong solutions of stochastic equations with singular time dependent drift
• Estimates for the density of functionals of SDEs with irregular drift
• The parametrix method for parabolic SPDEs
• Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients
• Gaussian estimates for elliptic operators with unbounded drift
• A representation formula for transition probability densities of diffusions and applications
• Two-sided estimates on the density of Brownian motion with singular drift
• The Malliavin Calculus and Related Topics
• On singular stochastic differential equations and Dirichlet forms
• On the stochastic regularity of distorted Brownian motions