In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically di...In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.展开更多
Objective:The purpose of this study was to determine the effectiveness of brisk walking as an intervention for self-care agency and care dependency in patients with permanent colorectal cancer stoma.Method:This study ...Objective:The purpose of this study was to determine the effectiveness of brisk walking as an intervention for self-care agency and care dependency in patients with permanent colorectal cancer stoma.Method:This study adopted a quasi-experimental research design,specifically a non-equivalent control group pre-test and post-test design.Utilizing the Exercise of Self-Care Agency Scale(ESCA)and Care Dependency Scale(CDS),a survey was administered to 64 patients from a hospital in Shandong Province.The statistical methods used for analyzing data included frequency,mean,standard deviation(SD),independent t-test,P-value calculation,and dependent t-test.Result:After two months of a brisk walking exercise program,participants in the experimental group had a higher level of self-care agency than before the experiment(P<0.05),and their level of care dependency was significantly reduced(P<0.05).Participants in the control group also showed higher levels of self-care agency(P<0.05)and lower levels of care dependency(P<0.05)after two months compared to their levels before the two months.Conclusion:The brisk walking program had a positive impact on patients’self-care agency and reduced their care dependency.展开更多
A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory： the jumping distance and the waiting time, are ...A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory： the jumping distance and the waiting time, are replaced by two new ones： the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement （x^2（t）） - t^a is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0 〈 a 〈 2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.展开更多
We propose a solution method of Time Dependent Schr?dinger Equation (TDSE) and the advection equation by quantum walk/quantum cellular automaton with spatially or temporally variable parameters. Using numerical method...We propose a solution method of Time Dependent Schr?dinger Equation (TDSE) and the advection equation by quantum walk/quantum cellular automaton with spatially or temporally variable parameters. Using numerical method, we establish the quantitative relation between the quantum walk with the space dependent parameters and the “Time Dependent Schr?dinger Equation with a space dependent imaginary diffusion coefficient” or “the advection equation with space dependent velocity fields”. Using the 4-point-averaging manipulation in the solution of advection equation by quantum walk, we find that only one component can be extracted out of two components of left-moving and right-moving solutions. In general it is not so easy to solve an advection equation without numerical diffusion, but this method provides perfectly diffusion free solution by virtue of its unitarity. Moreover our findings provide a clue to find more general space dependent formalisms such as solution method of TDSE with space dependent resolution by quantum walk.展开更多
We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the ligh...We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.展开更多
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the proce...We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.展开更多
基金Research supported by National Science Foundation of China (70671018 and 10371117)
文摘In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.
文摘Objective:The purpose of this study was to determine the effectiveness of brisk walking as an intervention for self-care agency and care dependency in patients with permanent colorectal cancer stoma.Method:This study adopted a quasi-experimental research design,specifically a non-equivalent control group pre-test and post-test design.Utilizing the Exercise of Self-Care Agency Scale(ESCA)and Care Dependency Scale(CDS),a survey was administered to 64 patients from a hospital in Shandong Province.The statistical methods used for analyzing data included frequency,mean,standard deviation(SD),independent t-test,P-value calculation,and dependent t-test.Result:After two months of a brisk walking exercise program,participants in the experimental group had a higher level of self-care agency than before the experiment(P<0.05),and their level of care dependency was significantly reduced(P<0.05).Participants in the control group also showed higher levels of self-care agency(P<0.05)and lower levels of care dependency(P<0.05)after two months compared to their levels before the two months.Conclusion:The brisk walking program had a positive impact on patients’self-care agency and reduced their care dependency.
基金supported by the Scientific Research Foundation of Sichuan University for Young Teachers,China (GrantNo. 2009SCU11120)
文摘A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory： the jumping distance and the waiting time, are replaced by two new ones： the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement （x^2（t）） - t^a is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0 〈 a 〈 2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.
基金supported in part by TUT Programs on Advanced Simulation Engineering,Toyohashi University of Technology.
文摘We propose a solution method of Time Dependent Schr?dinger Equation (TDSE) and the advection equation by quantum walk/quantum cellular automaton with spatially or temporally variable parameters. Using numerical method, we establish the quantitative relation between the quantum walk with the space dependent parameters and the “Time Dependent Schr?dinger Equation with a space dependent imaginary diffusion coefficient” or “the advection equation with space dependent velocity fields”. Using the 4-point-averaging manipulation in the solution of advection equation by quantum walk, we find that only one component can be extracted out of two components of left-moving and right-moving solutions. In general it is not so easy to solve an advection equation without numerical diffusion, but this method provides perfectly diffusion free solution by virtue of its unitarity. Moreover our findings provide a clue to find more general space dependent formalisms such as solution method of TDSE with space dependent resolution by quantum walk.
基金Acknowledgements The authors would like to thank Drs. Hongyan Sun and Ke Zhou for their stimulating discussion. Also they would like to express their gratitude to the referees for their careful reading of the first version of paper and useful suggestions for revising the paper. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11131003）, the 985 Project, and the Natural Sciences and Engineering Research Council of Canada （Grant No. 315660）.
文摘We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.
基金the National Natural Sciente Foundation of China (Grant Nos. 10771021, 10471012)Scientific Research Foundation for Returned Scholars, Ministry of Education of China (Grant No. [2005]564)
文摘We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.
