Monotonicity and convergence for g-expectation of distributions

Abstract

Based on the g-expectation of distributions, we obtain the monotonicity and Jensen’s inequality for the g-expectation of distributions; and for a sequence of distribution functions, we establish a monotone weak convergence theorem, Fatou’s lemma, and a convergence theorem with respect to the g-expectation of distributions.

Keywords

g-expectation / g-expectation of distributions / Backward stochastic differential equation / Monotonicity / Monotone weak convergence / Convergence

Acknowledgements

The authors acknowledge financial support from the Fundamental Research Funds for the Central Universities (Grant No. 2024KYJD2008). The authors would like to thank the editor and the referee for their very careful reading of this paper and valuable comments and suggestions.

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