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 establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L'ibor [1].Then p-uniformly smoothable Banach space is c...In this paper,we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L'ibor [1].Then p-uniformly smoothable Banach space is characterized in terms of the Hàjek-Rèniy type inequality for Banach space valued martingales.Those results generalize the recent results of Gan Shixin [2].展开更多
In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities...In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.展开更多
In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and ...In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W∞^＊-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in [12] makes the proof elegant and evident.展开更多
Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it&#...Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it'sDoob's Decomposition: f= Z + A, where Z is a martingale in L1 and A is a nonnegativeincrasing and predictable process.(ii) There exists positive constants c, to such that > to.When 1 =2 the condition (ii) above is equivalent to the classical condition p < 1. Asa consequence, for a concave function ,if and only if E1(Mf) < cE2(Zo+A)for every nonnegative submartingale f.展开更多
In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditio...In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space.The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent.In particular,we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities.Finally,we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p>1.展开更多
In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities,...In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities, A(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.展开更多
Generally, super Brownian motion will not c on verge vaguely to 0 if the initial measure is sufficiet large, so it is very inte resting to get asymptotic estimation for super Brownian motion. In this paper, w e will p...Generally, super Brownian motion will not c on verge vaguely to 0 if the initial measure is sufficiet large, so it is very inte resting to get asymptotic estimation for super Brownian motion. In this paper, w e will prove two asymptotic for super Brownian motion with general critical bran ching mechanism.展开更多
The theme in this article is the inequalities of B_valued martingales and the properties of Banach spaces. In utilising the techniques of rearranged functions, we proved that for a martingale f we have ‖M αf‖ Φ...The theme in this article is the inequalities of B_valued martingales and the properties of Banach spaces. In utilising the techniques of rearranged functions, we proved that for a martingale f we have ‖M αf‖ Φ≤C pΦ ‖f # α‖ Φ and the same result for (Mf,S (p) (f)+D ∞), (Mf∧Sf,Mf∧Sf+D ∞). This contains the results in R.L.Long[1], furthermore, some of the inequalities can be used to describe the properties of Banach spaces.展开更多
This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and...This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and martingale inequalities to obtain expressions for the ruin probability as well as both expo- nential and non-exponential upper bounds for the ruin probability for an infinite time horizon. Numerical re- sults are included to illustrate the accuracy of the non-exponential bound.展开更多
An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying MΔ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martin...An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying MΔ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale spaces.展开更多
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 Youth Foundation of the Department of Education of Sichuan Province（07ZB042） Supported by Natural Science Foundation of the Department of Education of Sichuan Province（09ZC071）
文摘In this paper,we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L'ibor [1].Then p-uniformly smoothable Banach space is characterized in terms of the Hàjek-Rèniy type inequality for Banach space valued martingales.Those results generalize the recent results of Gan Shixin [2].
基金This work was supported by the NSF of China and the aid financial plan for the backbone of the young teachers of University of Henan
文摘In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.
基金supported by the NSF of China and the aid financial plan for the backbone of the young teachers of university of Henan
文摘In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W∞^＊-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in [12] makes the proof elegant and evident.
文摘Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it'sDoob's Decomposition: f= Z + A, where Z is a martingale in L1 and A is a nonnegativeincrasing and predictable process.(ii) There exists positive constants c, to such that > to.When 1 =2 the condition (ii) above is equivalent to the classical condition p < 1. Asa consequence, for a concave function ,if and only if E1(Mf) < cE2(Zo+A)for every nonnegative submartingale f.
文摘In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space.The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent.In particular,we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities.Finally,we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p>1.
文摘In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities, A(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.
文摘Generally, super Brownian motion will not c on verge vaguely to 0 if the initial measure is sufficiet large, so it is very inte resting to get asymptotic estimation for super Brownian motion. In this paper, w e will prove two asymptotic for super Brownian motion with general critical bran ching mechanism.
文摘The theme in this article is the inequalities of B_valued martingales and the properties of Banach spaces. In utilising the techniques of rearranged functions, we proved that for a martingale f we have ‖M αf‖ Φ≤C pΦ ‖f # α‖ Φ and the same result for (Mf,S (p) (f)+D ∞), (Mf∧Sf,Mf∧Sf+D ∞). This contains the results in R.L.Long[1], furthermore, some of the inequalities can be used to describe the properties of Banach spaces.
基金Supported by the National Natural Science Foundation of China (Nos. 19831020 and 70003002) and the Fundamental Research Foundation of School of Economics and Management,Tsinghua University
文摘This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and martingale inequalities to obtain expressions for the ruin probability as well as both expo- nential and non-exponential upper bounds for the ruin probability for an infinite time horizon. Numerical re- sults are included to illustrate the accuracy of the non-exponential bound.
基金the National Natural Science Foundation of China (Grant No. 10671147)
文摘An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying MΔ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale spaces.
