g-Expectation for Conformable Backward Stochastic Differential Equations

Axioms

Michal Fečkan¹  Mei Luo²  Jin-Rong Wang²  Donal O’Regan³ 

[1] Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia;Department of Mathematics, Guizhou University, Guiyang 550025, China;School of Mathematical and Statistical Sciences, National University of Ireland, 999014 Galway, Ireland;

关键词: nonlinear expectation;    g-expectation;    Doob–Meyer decomposition theorem;   

DOI  :  10.3390/axioms11020075

来源: DOAJ

【 摘 要 】

In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator g. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases.

【 授权许可】

Unknown