2022/10/27 by Khoa Lê, Lê, Khoa · 1 citation
Economics, Econometrics and Finance · #60G07 (Primary) #60H10 (Secondary) #60H35 #60H50 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2210.15736
openalex publication_date 2022/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stroock and Varadhan in 1997 and Geiss in 2005 independently introduced stochastic processes with bounded mean oscillation (BMO) and established their exponential integrability with some unspecified exponential constant. This result is an analogue of the John--Nirenberg inequality for functions of bounded mean oscillation. In this work, we quantify the size of the exponential constant by the modulus of mean oscillation. Some new applications of BMO processes in rough stochastic differential equations, numerical approximations and regularization by noise are discussed.