Proves the existence of supremum and infimum in the noncompact fuzzy number space E ～, redefines E ～ valued (M) integral, and then discusses the relations between (M) integral and (G) integral of E ～ valued functions.
In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜...In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.展开更多
Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the...Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.展开更多
Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools ar...Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.展开更多
文摘Proves the existence of supremum and infimum in the noncompact fuzzy number space E ～, redefines E ～ valued (M) integral, and then discusses the relations between (M) integral and (G) integral of E ～ valued functions.
基金Supported by the National Natural Science Foundation of China (10671176, 10771192, 70871103)
文摘In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(12ZB082)the Scientific research cultivation project of Sichuan University of Science&Engineering(2013PY07)+1 种基金the Scientific Research Fund of Shanghai University of Finance and Economics(2017110080)the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing(2018QZJ01)
文摘Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.
文摘Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
