Strict positivity of the density for simple jump processes using the tools of support theorems. Application to the Kac equation without cutoff

DOI10.1214/aop/1020107763zbMath1017.60063OpenAlexW1984011986MaRDI QIDQ1872254

Nicolas Fournier

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1020107763

zbMATH Keywords

Malliavin calculussupport theoremjump processesKac equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items

Quantitative Lower Bounds for the Full Boltzmann Equation, Part I: Periodic Boundary Conditions ⋮ Global Solution for the Spatially Inhomogeneous Non-cutoff Kac Equation ⋮ Supports for degenerate stochastic differential equations with jumps and applications ⋮ A criterium for the strict positivity of the density of the law of a Poisson process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exponential decay of the heat kernel over the diagonal. II
• Malliavin calculus for white noise driven parabolic SPDEs
• Asymptotic behavior of the transition density for jump type processes in small time
• Points of positive density for the solution to a hyperbolic SPDE
• Density in small time at accessible points for jump processes
• Strict positivity of a solution to a one-dimensional Kac equation without cutoff
• Probabilistic interpretation and numerical approximation of a Kac equation without cutoff
• Existence and regularity of a solution of a Kac equation without cutoff using the stochastic calculus of variations
• Support theorem for jump processes.
• Existence and regularity study for two-dimensional Kac equation without cutoff by a probabilistic approach.
• A Maxwellian lower bound for solutions to the Boltzmann equation
• Probabilistic treatment of the Boltzmann equation of Maxwellian molecules
• Strict positivity of the density for a poisson driven S.D.E
• Support theorem for the solution of a white-noise-driven parabolic stochastic partial differential equation with temporal Poissonian jumps
• Strict positivity of the solution to a 2-dimensional spatially homogeneous Boltzmann equation without cutoff