Work

SDEs with critical time dependent drifts: Weak solutions

Year: 2022

Type: article

Abstract: For d≥3, we prove that time-inhomogeneous stochastic differential equations driven by additive noises with drifts in critical Lebesgue space Lq([0,T];Lp(Rd)), where (p,q)∈(d,∞]×[2,∞) and d∕p+2∕q=1, or (p,q)=(d,∞) and divb∈L∞([0,T];Ld∕2+ε(Rd)), are well-posed. The weak uniqueness is obtained by solving corresponding Kolmogorov backward equations in some second-order Sobolev spaces, which is analytically interesting in itself.

Source: Bernoulli

DOI: 10.3150/22-bej1478

Authors: Michael Röckner, Guohuan Zhao

Institutions: Chinese Academy of Sciences, Bielefeld University, Academy of Mathematics and Systems Science

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funders: Deutsche Forschungsgemeinschaft, Universität Bielefeld

OpenAlex ID: W4306158338