In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion ...In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion.展开更多
Because single trigger system is unreliable for shock wave overpressure test, this paper presents a multi-trigger overpressure test system. The large memory capacity is divided into parts to achieve data acquisition a...Because single trigger system is unreliable for shock wave overpressure test, this paper presents a multi-trigger overpressure test system. The large memory capacity is divided into parts to achieve data acquisition and storage with multiple triggers. Compared with conventional single-shot storage test system, this system can prevent false trigger and improve reliability of the test. By using explosion time to extract valid signal segments, it improves the efficiency of data recovery. These characteristics of the system contribute to multi-point test. After the dynamic characteristics of the system are calibrated, the valid data can be obtained in explosion experiments. The results show that the multi-trigger test system has higher reliability than single trigger test system.展开更多
In this paper,we study the distribution function of the time of explosion of a stochastic differential equation modeling the length of the dominant crack due to fatigue.The main novelty is that initial condition is re...In this paper,we study the distribution function of the time of explosion of a stochastic differential equation modeling the length of the dominant crack due to fatigue.The main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward sense.Under suitable conditions,we use the substitution formula from Russo and Vallois to find the local solution of this equation.Then,we find the law of blow up time by proving some results on barrier crossing probabilities of Brownian bridge.展开更多
A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction tim...A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states.Regularity and uniqueness criteria are firstly established.Explicit expressions are then obtained for the extinction probability vector,the mean extinction times and the conditional mean extinction times.The explosion behavior of these models is investigated and an explicit expression for mean explosion time is established.The mean global holding time is also obtained.It is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.展开更多
We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant ...We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness, Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed.The mean explosion time and the total mean life time of th, processes are also investigated and resolved.展开更多
基金Supported in part by National Natural Science Foundation of China (Grant Nos. 10901065,60934009)
文摘In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion.
文摘Because single trigger system is unreliable for shock wave overpressure test, this paper presents a multi-trigger overpressure test system. The large memory capacity is divided into parts to achieve data acquisition and storage with multiple triggers. Compared with conventional single-shot storage test system, this system can prevent false trigger and improve reliability of the test. By using explosion time to extract valid signal segments, it improves the efficiency of data recovery. These characteristics of the system contribute to multi-point test. After the dynamic characteristics of the system are calibrated, the valid data can be obtained in explosion experiments. The results show that the multi-trigger test system has higher reliability than single trigger test system.
文摘In this paper,we study the distribution function of the time of explosion of a stochastic differential equation modeling the length of the dominant crack due to fatigue.The main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward sense.Under suitable conditions,we use the substitution formula from Russo and Vallois to find the local solution of this equation.Then,we find the law of blow up time by proving some results on barrier crossing probabilities of Brownian bridge.
基金supported by National Natural Science Foundation of China (Grant No.10771216)Research Grants Council of Hong Kong (Grant No.HKU 7010/06P)Scientific Research Foundation for Returned Overseas Chinese Scholars,State Education Ministry of China (Grant No.[2007]1108)
文摘A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states.Regularity and uniqueness criteria are firstly established.Explicit expressions are then obtained for the extinction probability vector,the mean extinction times and the conditional mean extinction times.The explosion behavior of these models is investigated and an explicit expression for mean explosion time is established.The mean global holding time is also obtained.It is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.
基金supported by National Natural Science Foundation of China (Grant Nos 11371374 and 11571372)Research Fund for the Doctoral Program of Higher Education of China (Grant No 20110162110060)
文摘We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness, Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed.The mean explosion time and the total mean life time of th, processes are also investigated and resolved.
