In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria...In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.展开更多
In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are o...In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.展开更多
Assembly path planning is a crucial problem in assembly related design and manufacturing processes. Sampling based motion planning algorithms are used for computational assembly path planning. However, the performance...Assembly path planning is a crucial problem in assembly related design and manufacturing processes. Sampling based motion planning algorithms are used for computational assembly path planning. However, the performance of such algorithms may degrade much in environments with complex product structure, narrow passages or other challenging scenarios. A computational path planner for automatic assembly path planning in complex 3D environments is presented. The global planning process is divided into three phases based on the environment and specific algorithms are proposed and utilized in each phase to solve the challenging issues. A novel ray test based stochastic collision detection method is proposed to evaluate the intersection between two polyhedral objects. This method avoids fake collisions in conventional methods and degrades the geometric constraint when a part has to be removed with surface contact with other parts. A refined history based rapidly-exploring random tree （RRT） algorithm which bias the growth of the tree based on its planning history is proposed and employed in the planning phase where the path is simple but the space is highly constrained. A novel adaptive RRT algorithm is developed for the path planning problem with challenging scenarios and uncertain environment. With extending values assigned on each tree node and extending schemes applied, the tree can adapts its growth to explore complex environments more efficiently. Experiments on the key algorithms are carried out and comparisons are made between the conventional path planning algorithms and the presented ones. The comparing results show that based on the proposed algorithms, the path planner can compute assembly path in challenging complex environments more efficiently and with higher success. This research provides the references to the study of computational assembly path planning under complex environments.展开更多
In this paper,we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions.We may apply it to a class of stochastic differential equations with the kernel of fractional Bro...In this paper,we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions.We may apply it to a class of stochastic differential equations with the kernel of fractional Brownian motion with Hurst parameter H∈(1/2,1)and subfractional Brownian motion with Hurst parameter H∈(1/2,1).As far as we know,this is the first result on stochastic Volterra equations in this topic.展开更多
In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to...In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.展开更多
Stochastic differential equation (SDE) is an ordinary differential equation with a stochastic process that can model the unpredictable real-life behavior of any continuous systems. It is the combination of differentia...Stochastic differential equation (SDE) is an ordinary differential equation with a stochastic process that can model the unpredictable real-life behavior of any continuous systems. It is the combination of differential equations, probability theory, and stochastic processes. Stochastic differential equations arise in modeling a variety of random dynamic phenomena in physical, biological and social process. The SDE theory is traditionally used in physical science and financial mathematics. Recently, more researchers have been conducted in the application of SDE theory to various areas of engineering. This dissertation is mainly concerned with the existence of mild solutions for impulsive neutral stochastic differential equations with nonlocal conditions in Hilbert spaces. The results are obtained by using fractional powers of operator in the semigroup theory and Sadovskii fixed point theorem.展开更多
For solving the stochastic differential equations driven by fractional Brownian motion,we present the modified split-step theta method by combining truncated Euler-Maruyama method with split-step theta method.For the ...For solving the stochastic differential equations driven by fractional Brownian motion,we present the modified split-step theta method by combining truncated Euler-Maruyama method with split-step theta method.For the problem under a locally Lipschitz condition and a linear growth condition,we analyze the strong convergence and the exponential stability of the proposed method.Moreover,for the stochastic delay differential equations with locally Lipschitz drift condition and globally Lipschitz diffusion condition,we give the order of convergence.Finally,numerical experiments are done to confirm the theoretical conclusions.展开更多
In this paper,a stochastic SiS epidemic infectious diseases model with double stochastic perturbations is proposed.First,the existence and uniqueness of the positive global solution of the model are proved.Second,the ...In this paper,a stochastic SiS epidemic infectious diseases model with double stochastic perturbations is proposed.First,the existence and uniqueness of the positive global solution of the model are proved.Second,the controlling conditions for the extinction and persistence of the disease are obtained.Besides,the effects of the intensity of volatility Si and the speed of reversion 1 on the dynamical behaviors of the model are discussed.Finally,some numerical examples are given to support the theoretical results.The results show that if the basic reproduction number R_(0)^(8)<1,the disease will be extinct,that is to say that we can control the threshold R_(0)^(8)to suppress the disease outbreak.展开更多
We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set...We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10171009) Tianyuan Young Fund of China (Grant No. 10226009).
文摘In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.
基金the National Natural Science Foundation of China(No.10571092)
文摘In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.
基金supported by National Natural Science Foundation of China(Grant No. 51275047)Fund of National Engineering and Research Center for Commercial Aircraft Manufacturing of China(Grant No. 07205)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No. 20091101110010)
文摘Assembly path planning is a crucial problem in assembly related design and manufacturing processes. Sampling based motion planning algorithms are used for computational assembly path planning. However, the performance of such algorithms may degrade much in environments with complex product structure, narrow passages or other challenging scenarios. A computational path planner for automatic assembly path planning in complex 3D environments is presented. The global planning process is divided into three phases based on the environment and specific algorithms are proposed and utilized in each phase to solve the challenging issues. A novel ray test based stochastic collision detection method is proposed to evaluate the intersection between two polyhedral objects. This method avoids fake collisions in conventional methods and degrades the geometric constraint when a part has to be removed with surface contact with other parts. A refined history based rapidly-exploring random tree （RRT） algorithm which bias the growth of the tree based on its planning history is proposed and employed in the planning phase where the path is simple but the space is highly constrained. A novel adaptive RRT algorithm is developed for the path planning problem with challenging scenarios and uncertain environment. With extending values assigned on each tree node and extending schemes applied, the tree can adapts its growth to explore complex environments more efficiently. Experiments on the key algorithms are carried out and comparisons are made between the conventional path planning algorithms and the presented ones. The comparing results show that based on the proposed algorithms, the path planner can compute assembly path in challenging complex environments more efficiently and with higher success. This research provides the references to the study of computational assembly path planning under complex environments.
基金support provided by the Key Scientific Research Project Plans of Henan Province Advanced Universities(No.24A110006)the NSFs of China(Grant Nos.11971154,12361030)by the Science and Technology Foundation of Jiangxi Education Department(Grant No.GJJ190265)。
文摘In this paper,we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions.We may apply it to a class of stochastic differential equations with the kernel of fractional Brownian motion with Hurst parameter H∈(1/2,1)and subfractional Brownian motion with Hurst parameter H∈(1/2,1).As far as we know,this is the first result on stochastic Volterra equations in this topic.
文摘In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.
文摘Stochastic differential equation (SDE) is an ordinary differential equation with a stochastic process that can model the unpredictable real-life behavior of any continuous systems. It is the combination of differential equations, probability theory, and stochastic processes. Stochastic differential equations arise in modeling a variety of random dynamic phenomena in physical, biological and social process. The SDE theory is traditionally used in physical science and financial mathematics. Recently, more researchers have been conducted in the application of SDE theory to various areas of engineering. This dissertation is mainly concerned with the existence of mild solutions for impulsive neutral stochastic differential equations with nonlocal conditions in Hilbert spaces. The results are obtained by using fractional powers of operator in the semigroup theory and Sadovskii fixed point theorem.
基金supported by the National Natural Science Foundation of China(Project No.12071100)Funds for the Central Universities(Project No.2022FRFK060019).
文摘For solving the stochastic differential equations driven by fractional Brownian motion,we present the modified split-step theta method by combining truncated Euler-Maruyama method with split-step theta method.For the problem under a locally Lipschitz condition and a linear growth condition,we analyze the strong convergence and the exponential stability of the proposed method.Moreover,for the stochastic delay differential equations with locally Lipschitz drift condition and globally Lipschitz diffusion condition,we give the order of convergence.Finally,numerical experiments are done to confirm the theoretical conclusions.
基金supported by National Science and Technology Innovation 2030 of China Next-Generation Artificial Intelligence Major Project(Grant No.2018AAA0101800)Key Project of Technological Innovation and Application Development Plan of Chongqing(Grant No.cstc2020jscx-dxwtBX0044)+1 种基金Key projects of Mathematics and Finance Research Center of Sichuan University of Arts and Science(No.SCMF202201)National College Students Innovation and Entrepreneurship Training Program(No.S202110619028,202210619035).
文摘In this paper,a stochastic SiS epidemic infectious diseases model with double stochastic perturbations is proposed.First,the existence and uniqueness of the positive global solution of the model are proved.Second,the controlling conditions for the extinction and persistence of the disease are obtained.Besides,the effects of the intensity of volatility Si and the speed of reversion 1 on the dynamical behaviors of the model are discussed.Finally,some numerical examples are given to support the theoretical results.The results show that if the basic reproduction number R_(0)^(8)<1,the disease will be extinct,that is to say that we can control the threshold R_(0)^(8)to suppress the disease outbreak.
基金the Deanship of Scientific Research at King Khalid University for funding their work through Research Group Program under grant number(G.P.1/160/40)。
文摘We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.
