Invariance properties of Brownian motion via Lie's symmetries
Susanna Deh\`o, Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
TL;DR
This paper explores the invariance properties of Brownian motion using Lie symmetry methods for stochastic differential equations, revealing key properties through a novel integration by parts formula.
Contribution
It introduces a Lie symmetry approach to analyze Brownian motion invariance properties, providing new insights and tools for stochastic differential equations.
Findings
Recovered notable invariance properties of Brownian motion
Developed a related integration by parts formula
Enhanced understanding of stochastic symmetries
Abstract
The invariance properties of Brownian motion are investigated and revisited within a recent Lie symmetry approach to stochastic differential equations. Some notable properties of the process can be recovered by a related integration by parts formula developed in the same research area.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · stochastic dynamics and bifurcation · Statistical Mechanics and Entropy