To the Editor:The unprecedented pandemic of coronavirus disease 2019(COVID-19)has put tremendous pressure on healthcare resources and economic development worldwide.Severe acute respiratory syndrome coronavirus 2(SARS...To the Editor:The unprecedented pandemic of coronavirus disease 2019(COVID-19)has put tremendous pressure on healthcare resources and economic development worldwide.Severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)Omicron strain has become the dominant causative strain of COVID-19 in most countries since the end of 2021.Although a large cohort study comparing the symptomatic presentation of SARSCoV-2 Omicron and Delta infection has been made in the UK,[1]features and evolution of symptoms of individuals infected with Omicron are rarely reported in other countries or regions,especially among Asian individuals.展开更多
In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drif...In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drift coefficients. We study regularity properties of the solutions of this kind of BSDEs and establish their connection with semi-linear backward parabolic partial differential equations in simplex with Neumann boundary condition. As an application, we study the European option pricing problem with capital size based stock prices.展开更多
Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and the...Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and then study the pseudo almost automorphic solution in the distribution sense to stochastic differential equation driven by Levy process.展开更多
文摘To the Editor:The unprecedented pandemic of coronavirus disease 2019(COVID-19)has put tremendous pressure on healthcare resources and economic development worldwide.Severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)Omicron strain has become the dominant causative strain of COVID-19 in most countries since the end of 2021.Although a large cohort study comparing the symptomatic presentation of SARSCoV-2 Omicron and Delta infection has been made in the UK,[1]features and evolution of symptoms of individuals infected with Omicron are rarely reported in other countries or regions,especially among Asian individuals.
基金supported by National Science Foundation of USA(Grant No.DMS-1206276)National Natural Science Foundation of China(Grant No.11601280)
文摘In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drift coefficients. We study regularity properties of the solutions of this kind of BSDEs and establish their connection with semi-linear backward parabolic partial differential equations in simplex with Neumann boundary condition. As an application, we study the European option pricing problem with capital size based stock prices.
基金The authors are grateful to the anonymous referees for very helpful comments on the original version of this paper. The work of Xinwei FENG was partially supported by the National Natural Science Foundation of China （Grant No. 11601280）. The work of Gaofeng ZONG was supported in part by the National Natural Science Foundation of China （Grant Nos. 11501325, 11231005） and the China Postdoctoral Science Foundation （Grant No. 2018T110706）.
文摘Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and then study the pseudo almost automorphic solution in the distribution sense to stochastic differential equation driven by Levy process.
