L\'evy Flows and associated Stochastic PDEs
Arvind Kumar Nath (1), Suprio Bhar (1) ((1) Indian Institute of, Technology Kanpur)
TL;DR
This paper investigates the structural properties of Lévy flows to establish the existence and uniqueness of strong solutions for a class of stochastic PDEs driven by Lévy noise, extending previous diffusion case results.
Contribution
It introduces new methods to prove existence and uniqueness of solutions for Lévy-driven stochastic PDEs, generalizing earlier diffusion-based findings.
Findings
Established existence of strong solutions for Lévy-driven SPDEs.
Proved uniqueness of solutions using Monotonicity inequality.
Extended previous diffusion case results to Lévy noise context.
Abstract
In this paper, we first explore certain structural properties of L\'evy flows and use this information to obtain the existence of strong solutions to a class of Stochastic PDEs in the space of tempered distributions, driven by L\'evy noise. The uniqueness of the solutions follows from Monotonicity inequality. These results extend an earlier work Bhar (2017) on the diffusion case.
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 · Nonlinear Differential Equations Analysis