$L^q$-valued Burkholder-Rosenthal inequalities and sharp estimates for stochastic integrals

Abstract

We prove sharp maximal inequalities for $L^q$-valued stochastic integrals with respect to any Hilbert space-valued local martingale. Our proof relies on new Burkholder-Rosenthal type inequalities for martingales taking values in an $L^q$-space.

References in corpus (3)

• Stochastic integration in UMD Banach spaces
• Cylindrical continuous martingales and stochastic integration in infinite dimensions
• Fourier multipliers and weak differential subordination of martingales in UMD Banach spaces

Cited by in corpus (2)

• Burkholder-Davis-Gundy inequalities in UMD Banach spaces
• Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes