Work

Multidimensional SDE with distributional drift and Lévy noise

Year: 2022

Type: article

Abstract: We solve multidimensional SDEs with distributional drift driven by symmetric, α-stable Lévy processes for α∈(1,2] by studying the associated (singular) martingale problem and by solving the Kolmogorov backward equation. We allow for drifts of regularity (2−2α)∕3, and in particular we go beyond the by now well understood “Young regime”, where the drift must have better regularity than (1−α)∕2. The analysis of the Kolmogorov backward equation in the low regularity regime is based on paracontrolled distributions. As an application of our results we construct a Brox diffusion with Lévy noise.

Source: Bernoulli

DOI: 10.3150/21-bej1394

Authors: Helena Kremp, Nicolas Perkowski

Institution: Freie Universität Berlin

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: Deutsche Forschungsgemeinschaft

Awards: G1372115314, G2033548659, G743358325