The transition point in the zero noise limit for a 1D Peano example

DOI10.3934/dcds.2014.34.4071zbMath1314.60113OpenAlexW1994840865MaRDI QIDQ476469

Franco Flandoli, François Delarue

Publication date: 2 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.4071

zbMATH Keywords

stochastic differential equationsnon-uniquenesssingular driftsPeano phenomenazero-noise limit

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Limit theorems in probability theory (60F99)

Related Items (13)

Zero noise limit of a stochastic differential equation involving a local time ⋮ On a selection problem for small noise perturbation in the multidimensional case ⋮ Weak regularization by stochastic drift: result and counter example ⋮ Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients ⋮ Zero-noise dynamics after collapse for three point vortices ⋮ A selection procedure for extracting the unique Feller weak solution of degenerate diffusions ⋮ Well-posedness by noise for scalar conservation laws ⋮ On regularization by a small noise of multidimensional odes with non-Lipschitz coefficients ⋮ Selection of equilibria in a linear quadratic mean-field game ⋮ Simultaneous small noise limit for singularly perturbed slow-fast coupled diffusions ⋮ Generalized Peano problem with Lévy noise ⋮ Strong regularization by Brownian noise propagating through a weak Hörmander structure ⋮ Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result

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