This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgen...This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.展开更多
In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable ob...In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].展开更多
In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result ...In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].展开更多
In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed...In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.展开更多
In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the nu...In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.展开更多
Let {X<sub>n</sub>, n≥1} be a sequence of random variables taking values in S={1,2,…} with the joint distribution f（x<sub>1</sub>,…, x<sub>n</sub>）=P（X<sub>1</sub>...Let {X<sub>n</sub>, n≥1} be a sequence of random variables taking values in S={1,2,…} with the joint distribution f（x<sub>1</sub>,…, x<sub>n</sub>）=P（X<sub>1</sub>=x<sub>1</sub>,…, X<sub>n</sub>=x<sub>n</sub>）】0, x<sub>i</sub>∈S,1≤i≤n.（1） It is easy to see that {X<sub>n</sub>, n≥l} are independent and identically distributed iff there exists a probability distibution on展开更多
This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive cons...This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.展开更多
针对国际学界提出的电网智能运行中风险限制调度的框架,新建考虑线路阻塞的风险限制调度多步整合模型,包括日前三步整合调度模型、时前两步整合调度模型和紧急调度模型。日前三步整合调度是在日前调度中计入预估的时前、紧急调度的随机...针对国际学界提出的电网智能运行中风险限制调度的框架,新建考虑线路阻塞的风险限制调度多步整合模型,包括日前三步整合调度模型、时前两步整合调度模型和紧急调度模型。日前三步整合调度是在日前调度中计入预估的时前、紧急调度的随机信息;时前两步整合调度计入了预估的紧急调度随机信息。随机信息主要考虑风电出力,并作为模型中的随机变量。通过定义线路阻塞条件风险(conditional value at risk,CVa R)值,将线路安全约束转化为线路阻塞风险限制约束,实现线路阻塞的风险限制调度。仿真结果表明:线路阻塞CVa R值的限值与置信水平两个值取值合理时,多步整合调度与传统的日前、时前、紧急三步调度相比运行成本较低;当前值限定在一定水平时,后值越大,多步整合调度的成本越高;后值一定时,前值越大,多步整合调度的成本越低。线路阻塞风险限制的多步整合调度模型是解决电力系统智能运行中风险限制调度的有效途径。展开更多
文摘This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.
文摘In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].
文摘In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].
基金Research supported by National Science Foundation of China(No.10071081)special financial support of Chinese Academy of Sciences
文摘In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.
文摘In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.
文摘Let {X<sub>n</sub>, n≥1} be a sequence of random variables taking values in S={1,2,…} with the joint distribution f（x<sub>1</sub>,…, x<sub>n</sub>）=P（X<sub>1</sub>=x<sub>1</sub>,…, X<sub>n</sub>=x<sub>n</sub>）】0, x<sub>i</sub>∈S,1≤i≤n.（1） It is easy to see that {X<sub>n</sub>, n≥l} are independent and identically distributed iff there exists a probability distibution on
文摘This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.
文摘针对国际学界提出的电网智能运行中风险限制调度的框架,新建考虑线路阻塞的风险限制调度多步整合模型,包括日前三步整合调度模型、时前两步整合调度模型和紧急调度模型。日前三步整合调度是在日前调度中计入预估的时前、紧急调度的随机信息;时前两步整合调度计入了预估的紧急调度随机信息。随机信息主要考虑风电出力,并作为模型中的随机变量。通过定义线路阻塞条件风险(conditional value at risk,CVa R)值,将线路安全约束转化为线路阻塞风险限制约束,实现线路阻塞的风险限制调度。仿真结果表明:线路阻塞CVa R值的限值与置信水平两个值取值合理时,多步整合调度与传统的日前、时前、紧急三步调度相比运行成本较低;当前值限定在一定水平时,后值越大,多步整合调度的成本越高;后值一定时,前值越大,多步整合调度的成本越低。线路阻塞风险限制的多步整合调度模型是解决电力系统智能运行中风险限制调度的有效途径。
