A quenched local limit theorem for stochastic flows

We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We impose no structural assumption (such as incompressibility) on the velocity field. We show that conditional on the velocity field, the quenched density of the particle after a long time can be approximated pointwise by the product of a deterministic Gaussian density and a spacetime-stationary random field.

A quenched local limit theorem for stochastic flows Alexander Dunlap* Yu Gu† December 10, 2021 arXiv:2105.07907v3 [math.PR] 8 Dec 2021 Abstract We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by…

related reading

• A Primer on Stochastic Partial Differential Equationsmath.utah.edu
• Brownian motion - Wikipediaen.wikipedia.org
• Research • Leonid Petrov. Integrable Probabilitylpetrov.cc
• statement.pdfcims.nyu.edu
• Density Dependent Singular Stochastic Differential Equationsarxiv.org
• Law of large numbers - Wikipediaen.wikipedia.org
• De Finetti's theorem - Wikipediaen.wikipedia.org
• refining bounds - cover timesarxiv.org
• 0907.4178arxiv.org
• Gregory Gundersengregorygundersen.com
• Dynamical Approach to RMT.pdfpeople.math.harvard.edu
• Stochastic process - Wikipediaen.wikipedia.org