REGULARIZING PROPERTIES OF BROWNIAN PATHS AND A RESULT OF DAVIE

DOI10.1142/S0219493711003310zbMath1236.60077OpenAlexW2000489949MaRDI QIDQ3173993

Franco Flandoli

Publication date: 11 October 2011

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493711003310

zbMATH Keywords

stochastic differential equationuniquenessBrownian motiondifferential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Sample path properties (60G17)

Related Items (13)

Noiseless regularisation by noise ⋮ Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functions ⋮ Davie's type uniqueness for a class of SDEs with jumps ⋮ On uniqueness for some non-Lipschitz SDE ⋮ Well-posedness of the deterministic transport equation with singular velocity field perturbed along fractional Brownian paths ⋮ Regularity of local times associated with Volterra-Lévy processes and path-wise regularization of stochastic differential equations ⋮ Stochastic differential equations with critically irregular drift coefficients ⋮ Example of a Dirichlet process whose zero energy part has finite \(p\)-th variation ⋮ Some Remarks on Davie’s Uniqueness Theorem ⋮ Stochastic regularization for transport equations ⋮ The second-order parabolic PDEs with singular coefficients and applications ⋮ Strong solutions of stochastic differential equations with square integrable drift ⋮ Strong regularization by Brownian noise propagating through a weak Hörmander structure

Cites Work

• Transport equation and Cauchy problem for BV vector fields
• Remarks on uniqueness and strong solutions to deterministic and stochastic differential equations
• Well-posedness of the transport equation by stochastic perturbation
• Ordinary differential equations, transport theory and Sobolev spaces
• Strong solutions of stochastic equations with singular time dependent drift
• Transport equations and multi-D hyperbolic conservation laws
• The Heat Equation inL_q((0,T),L_p)-Spaces with Weights
• Stochastic differential equations and stochastic flows of diffeomorphisms
• On Positive Solutions of the Equation $\mathfrak{A}U + Vu = 0$
• ON STRONG SOLUTIONS AND EXPLICIT FORMULAS FOR SOLUTIONS OF STOCHASTIC INTEGRAL EQUATIONS

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