Backward Doubly Stochastic Integral Equations of the Volterra Type and Some Related Problems

Abstract

Backward doubly stochastic integral equations of the Volterra type (BDSIEVs in short) are observed in this paper. Existence of M-solution established under functional Lipschitz assumptions. Duality principle between linear BDSIEVs and (forward) stochastic Volterra integral equations is obtained. Using duality principle, the comparison theorem for the adapted solutions of BDSIEVs is proven.

Keywords

Backward doubly stochastic Volterra integral equations / Adapted solutions / Duality principle / Comparison theorem / Mathematical Sciences / Statistics

Funding

STORM-Stochastics for Time-Space Risk Models, granted by Research Council of Norway-Independent projects: ToppForsk.(Project nr.274410)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature