In this paper we obtain the uniform bounds on the rate of convergence in the central limit theorem (CLT) for a class of two-parameter martingale difference sequences under certain conditions.
In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable expo...In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.展开更多
In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit ...In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality.To this end,we also present the integration by parts formula for such a measure,which is obtained via its pull back formula and the Bismut method.展开更多
This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the con...This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.展开更多
In this paper the regularity of set-valued martingales in the sense of JL is given first. Then we show some kinds of Doob's stopping theorems for set-valued (super, sub) martingales with continuous time.
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation ...In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.展开更多
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem ...The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.展开更多
In this paper, the central limit theorem for two-parameter martingale differences andstationary random fields is obtained. The martingale differences are defined according tothe order of the lattices (s_1,s_2)<(t_1...In this paper, the central limit theorem for two-parameter martingale differences andstationary random fields is obtained. The martingale differences are defined according tothe order of the lattices (s_1,s_2)<(t_1,t_2) iff s_1<t_1 or S_1=t_1 and s_2<t_2. An example showsthat this definition may be the weakest condition under which the central limit theorem stillholds. These results are used for the limit distribution of average value and sample autocovar-iances of stationary random fields as well as least squares estimates for some kind of spatialAR models.展开更多
The existence,uniqueness,and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are developed.The goal is to develop a general multi-asset framework encompassing a wide spectrum of...The existence,uniqueness,and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are developed.The goal is to develop a general multi-asset framework encompassing a wide spectrum of non-linear financial models with jumps,including as particular cases,the setups studied by Peng and Xu[27,28]and Dumitrescu et al.[7]who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.展开更多
文摘In this paper we obtain the uniform bounds on the rate of convergence in the central limit theorem (CLT) for a class of two-parameter martingale difference sequences under certain conditions.
基金supported by NSFC(11471251)supported by NSFC(11271293)
文摘In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.
基金supported by the National Natural Science Foundation of China(11801064)。
文摘In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality.To this end,we also present the integration by parts formula for such a measure,which is obtained via its pull back formula and the Bismut method.
文摘This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.
基金Supported by the National Natural Science Foundation of China !(19971072)
文摘In this paper the regularity of set-valued martingales in the sense of JL is given first. Then we show some kinds of Doob's stopping theorems for set-valued (super, sub) martingales with continuous time.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10671147)
文摘In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.
基金supported by National Natural Science Foundation of China(Grant No.11731012)the Fundamental Research Funds for the Central Universities+1 种基金the State Key Development Program for Basic Research of China(Grant No.2015CB352302)Zhejiang Provincial Natural Science Foundation(Grant No.LY17A010016)。
文摘The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.
文摘In this paper, the central limit theorem for two-parameter martingale differences andstationary random fields is obtained. The martingale differences are defined according tothe order of the lattices (s_1,s_2)<(t_1,t_2) iff s_1<t_1 or S_1=t_1 and s_2<t_2. An example showsthat this definition may be the weakest condition under which the central limit theorem stillholds. These results are used for the limit distribution of average value and sample autocovar-iances of stationary random fields as well as least squares estimates for some kind of spatialAR models.
基金the Australian Research Council Discovery Project(Grant No.DP200101550)The work of T.Nie was supported by the National Natural Science Foundation of China(Grant Nos.12022108,11971267,11831010,61961160732)Natural Science Foundation of Shandong Province(Grant Nos.ZR2019Z D42,ZR2020ZD24)。
文摘The existence,uniqueness,and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are developed.The goal is to develop a general multi-asset framework encompassing a wide spectrum of non-linear financial models with jumps,including as particular cases,the setups studied by Peng and Xu[27,28]and Dumitrescu et al.[7]who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.
