Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid...Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.展开更多
Due to irregular deployment of small base stations （SBSs）, the interference in cognitive heterogeneous networks （CHNs） becomes even more complex; in particular, the uncertainty of spectrum mobility aggravates the ...Due to irregular deployment of small base stations （SBSs）, the interference in cognitive heterogeneous networks （CHNs） becomes even more complex; in particular, the uncertainty of spectrum mobility aggravates the interference context. In this case, how to analyze system capacity to obtain a closed-form expression becomes a crucial problem. In this paper we employ stochastic methods to formulate the capacity of CHNs and achieve a closed-form expression. By using discrete-time Markov chains （DTMCs）, the spectrum mobility with respect to the arrival and departure of macro base station （MBS） users is modeled. Then an integral method is proposed to derive the interference based on stochastic geometry （SG）. Also, the effect of sensing accuracy on network capacity is discussed by concerning false-alarm and miss-detection events. Simulation results are illustrated to show that the proposed capacity analysis method for CHNs can approximate the conventional sum methods without rigorous requirement for channel station information （CSI）. Therefore, it turns out to be a feasible and efficient way to capture the network capacity in CHNs.展开更多
We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of re...We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.展开更多
This paper concerns with two reasons for stock price fluctuation, the instinctive stochastic fluctuation and the fluctuation caused by the spread of information. They are constructed by compound Poisson process and co...This paper concerns with two reasons for stock price fluctuation, the instinctive stochastic fluctuation and the fluctuation caused by the spread of information. They are constructed by compound Poisson process and continuum percolation model separately. Combining the two models, the authors get a Levy process for the price fluctuation that can explain the fat-tail phenomenon in stock market. The fat-tails axe also presented in numerical simulations.展开更多
文摘Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.
基金Project supported by the National Basic Research Program （973） of China （No. 2012CB315801）, the National Natural Science Foundation of China （Nos. 61302089 and 61302081）, and the State Major Science and Technology Special Projects （No. 2013ZX03001025-002）
文摘Due to irregular deployment of small base stations （SBSs）, the interference in cognitive heterogeneous networks （CHNs） becomes even more complex; in particular, the uncertainty of spectrum mobility aggravates the interference context. In this case, how to analyze system capacity to obtain a closed-form expression becomes a crucial problem. In this paper we employ stochastic methods to formulate the capacity of CHNs and achieve a closed-form expression. By using discrete-time Markov chains （DTMCs）, the spectrum mobility with respect to the arrival and departure of macro base station （MBS） users is modeled. Then an integral method is proposed to derive the interference based on stochastic geometry （SG）. Also, the effect of sensing accuracy on network capacity is discussed by concerning false-alarm and miss-detection events. Simulation results are illustrated to show that the proposed capacity analysis method for CHNs can approximate the conventional sum methods without rigorous requirement for channel station information （CSI）. Therefore, it turns out to be a feasible and efficient way to capture the network capacity in CHNs.
基金supported by National Natural Science Foundation of China (Grant Nos. 61573217,11471192 and 11626142)the National High-Level Personnel of Special Support Program,the Chang Jiang Scholar Program of Chinese Education Ministry+2 种基金the Natural Science Foundation of Shandong Province (Grant Nos. JQ201401 and ZR2016AB08)the Colleges and Universities Science and Technology Plan Project of Shandong Province (Grant No. J16LI55)the Fostering Project of Dominant Discipline and Talent Team of Shandong University of Finance and Economics
文摘We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.
基金supported by the Natural Science Foundation of Tianjin,China under Grant No.09JCYBLJC01800the China Postdoctoral Science Foundation Funded Project under Grant No.20110491248
文摘This paper concerns with two reasons for stock price fluctuation, the instinctive stochastic fluctuation and the fluctuation caused by the spread of information. They are constructed by compound Poisson process and continuum percolation model separately. Combining the two models, the authors get a Levy process for the price fluctuation that can explain the fat-tail phenomenon in stock market. The fat-tails axe also presented in numerical simulations.
