Regularity properties of jump diffusions with irregular coefficients

DOI10.1016/j.jmaa.2021.125220zbMath1471.35347arXiv1812.08001OpenAlexW3150413404MaRDI QIDQ2033163

Guohuan Zhao

Publication date: 14 June 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.08001

zbMATH Keywords

Lévy processstochastic flowMalliavin differentiabilityZvonkin's transformation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Maximal functions, Littlewood-Paley theory (42B25) Ordinary differential equations and systems with randomness (34F05) PDEs with randomness, stochastic partial differential equations (35R60) Strong solutions to PDEs (35D35) Jump processes on general state spaces (60J76)

Related Items

Nonlocal elliptic equation in Hölder space and the martingale problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic differential equations with Sobolev diffusion and singular drift and applications
• Stochastic differential equations with Sobolev drifts and driven by \(\alpha\)-stable processes
• A variational approach to the construction and Malliavin differentiability of strong solutions of SDEs
• Pathwise uniqueness for singular SDEs driven by stable processes
• The symbol associated with the solution of a stochastic differential equation
• Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients
• A priori estimates for integro-differential operators with measurable kernels
• Construction of strong solutions of SDE's via Malliavin calculus
• On the Cauchy problem for certain integro-differential operators in Sobolev and Hölder spaces
• Harnack inequalities for jump processes
• Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts
• Davie's type uniqueness for a class of SDEs with jumps
• On weak uniqueness and distributional properties of a solution to an SDE with \(\alpha\)-stable noise
• Stochastic flows for Lévy processes with Hölder drifts
• Strong solutions of stochastic equations with singular time dependent drift
• Perturbation of drift-type for Levy processes
• Schauder estimates for a class of non-local elliptic equations
• \(L^q(L^p)\)-theory of stochastic differential equations
• Stochastic Lagrangian path for Leray's solutions of 3D Navier-Stokes equations
• On the construction and Malliavin differentiability of solutions of Lévy noise driven SDE's with singular coefficients
• Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs
• Schauder estimates for drifted fractional operators in the supercritical case
• Sobolev differentiable stochastic flows for SDEs with singular coefficients: applications to the transport equation
• A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
• Heat kernel estimates for stable-like processes on \(d\)-sets.
• Lévy matters III. Lévy-type processes: construction, approximation and sample path properties
• Transition Probabilities for Symmetric Jump Processes
• Regularity theory for parabolic nonlinear integral operators
• Fourier Analysis and Nonlinear Partial Differential Equations
• The Euler-Maruyama method for S(F)DEs with Hölder drift and α-stable noise
• Weak uniqueness for SDEs driven by supercritical stable processes with Hölder drifts
• On the differentiability of the solution to an equation with drift and fractional diffusion
• On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes
• Stochastic flow for SDEs with jumps and irregular drift term
• Uniqueness of Solutions of Stochastic Differential Equations
• Holder estimates for solutions of integro differential equations like the fractional laplace
• Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order
• A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT