In a Euclidean space Rd, the Lebesgue-Stieltjes integral of set-valued stochastic processes with respect to real valued finite variation process is defined directly by employing all integrably bounded selections inste...In a Euclidean space Rd, the Lebesgue-Stieltjes integral of set-valued stochastic processes with respect to real valued finite variation process is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integral is measurable, continuous in t under the Hausdorff metric and L2-bounded.展开更多
P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion ,and gave a dynamic equation about the number of segments,...P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion ,and gave a dynamic equation about the number of segments, their boundaries and AR model orders for each segment, but did not give detailed solution for the equation. Because the solution for the equation is very complex, this paper investigates the solution, derives some recursive relations, simplifies the problem ,saves computation time and goes further into the segmentation of nonstationary stochastic process into piecewise stationary stochastic process.展开更多
A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equati...A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.展开更多
In this paper we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal d...In this paper we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal dimension for filtered stochastic signals. The discretization of continuous time processes through this random scheme allows us to find, numerically, the expected value, variance and correlation functions at any point of time. This alternative method for estimating the fractal dimension is easy to implement and requires no sophisticated routines. We use simulated data sets for stationary processes of the type Random Ornstein Uhlenbeck to graphically illustrate the results and compare them with those obtained whit the box counting theorem.展开更多
This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing...This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing a series of appropriate stochastic Lyapunov functions,the asymptotic behaviors around the equilibria of deterministic model are obtained,and we demonstrate that the stochastic system exists a stationary Markov process.Third,the conditions for persistence in the mean and extinction of the stochastic system are established.Finally,we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results.The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.展开更多
We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definit...In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the It5 type set-valued stochastic differential equation.展开更多
首先,设计了节点自适应传感半径调整算法(AASR,adaptive adjustment of sensing radius),通过节点自适应选择最佳的覆盖范围,有效地进行节点覆盖控制,减少节点能量虚耗,提高覆盖效率。其次,从调整效果、能量消耗和覆盖冗余度3个方面对...首先,设计了节点自适应传感半径调整算法(AASR,adaptive adjustment of sensing radius),通过节点自适应选择最佳的覆盖范围,有效地进行节点覆盖控制,减少节点能量虚耗,提高覆盖效率。其次,从调整效果、能量消耗和覆盖冗余度3个方面对节点自适应传感半径调整算法进行了模拟实验和分析。仿真结果表明,AASR能够有效提高节点生存时间,减少能量消耗,提高覆盖率。展开更多
文摘In a Euclidean space Rd, the Lebesgue-Stieltjes integral of set-valued stochastic processes with respect to real valued finite variation process is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integral is measurable, continuous in t under the Hausdorff metric and L2-bounded.
文摘P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion ,and gave a dynamic equation about the number of segments, their boundaries and AR model orders for each segment, but did not give detailed solution for the equation. Because the solution for the equation is very complex, this paper investigates the solution, derives some recursive relations, simplifies the problem ,saves computation time and goes further into the segmentation of nonstationary stochastic process into piecewise stationary stochastic process.
基金supported by the National Key R&D Program of China(2020YFA0712900)the National Natural Science Foundation of China(11531001).
文摘A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.
文摘In this paper we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal dimension for filtered stochastic signals. The discretization of continuous time processes through this random scheme allows us to find, numerically, the expected value, variance and correlation functions at any point of time. This alternative method for estimating the fractal dimension is easy to implement and requires no sophisticated routines. We use simulated data sets for stationary processes of the type Random Ornstein Uhlenbeck to graphically illustrate the results and compare them with those obtained whit the box counting theorem.
基金supported by the Research Fund for the Taishan Scholar Project of Shandong Province of China,Shandong Provincial Natural Science Foundation of China(ZR2019MA003)。
文摘This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing a series of appropriate stochastic Lyapunov functions,the asymptotic behaviors around the equilibria of deterministic model are obtained,and we demonstrate that the stochastic system exists a stationary Markov process.Third,the conditions for persistence in the mean and extinction of the stochastic system are established.Finally,we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results.The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.
基金This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Educationthe Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
文摘We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
基金Supported by National Natural Science Foundation of China (Grant No. 10771010), PHR (IHLB), Research Fund of Beijing Educational Committee, ChinaGrant-in-Aid for Scientific Research 19540140, Japan
文摘In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the It5 type set-valued stochastic differential equation.
文摘首先,设计了节点自适应传感半径调整算法(AASR,adaptive adjustment of sensing radius),通过节点自适应选择最佳的覆盖范围,有效地进行节点覆盖控制,减少节点能量虚耗,提高覆盖效率。其次,从调整效果、能量消耗和覆盖冗余度3个方面对节点自适应传感半径调整算法进行了模拟实验和分析。仿真结果表明,AASR能够有效提高节点生存时间,减少能量消耗,提高覆盖率。
