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15 December 2019, Volume 36 Issue 6 Previous Issue    Next Issue

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Parametric Estimation of Stochastic Volatility Models with Generalized Moment Method ZHANG Xin-jun, CHEN Hua-zhu, JIANG Liang 2019, 36 (6):  611-626.  doi: 10.3969/j.issn.1005-3085.2019.06.001 Abstract ( 413 )   PDF (259KB) ( 931 )   Save The risks of financial asset prices arise from their fluctuation, which can be defined by volatility. This paper develops the Generalized Moment Method (GMM) to make parametric estimations and statistical inference for stochastic volatility models by using the Shanghai Composite Index. By utilizing the infinitesimal generator, the conditional expectation operator and the Taylor expansion of the differential operator, we determine the necessary conditions for GMM, namely, the orthogonal moment condition. Meanwhile, the filtered values of the stochastic volatility will be estimated by developing a sampling-importance and resampling algorithm. The empirical results show that the established model needs to introduce stochastic volatility, and the model can describe some major economic phenomena. Finally, we carry out the numerical results for European call option by using Monte Carlo method. Related Articles | Metrics

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Study on Energy-saving Operation of Subway Train Dispatching GONG Su-wen 2019, 36 (6):  627-636.  doi: 10.3969/j.issn.1005-3085.2019.06.002 Abstract ( 495 )   PDF (478KB) ( 518 )   Save We study the subway train dispatching problem based on energy-saving operation in this paper. By using the optimized dispatch method, the energy is saved. The optimization model is established by analyzing the forces of subway train and the undulate of railway track. Simulation of the model is run in Matlab to find an optimal operating diagram. Maximum principle, nonlinear equation model, and multi-objective programming are used to find the best combination of subway train speed and movement and time. Related Articles | Metrics

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Weighted-residual Based Detection Methods for Gradual Structure-changes in Linear Models ZHAO Wen-zhi, XIA Zhi-ming 2019, 36 (6):  637-646.  doi: 10.3969/j.issn.1005-3085.2019.06.003 Abstract ( 355 )   PDF (266KB) ( 426 )   Save In this paper, we study how to detect gradual changes in linear models. Firstly, the test statistics based on the weighted residual part and the weighted-CUSUM are proposed. Secondly, it is proved that the test statistics converge in distribution to the standard Brownian bridge under the original assumption, converge in distribution to the Brownian bridge with a drift term under the alternative hypothesis. The conditions for the test consistence are also given. Finally, simulation results show that the proposed method is feasible. Related Articles | Metrics

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Existence and Multiplicity of Solutions to a Class of Klein-Gordon-Maxwell System CHEN Li-zhen, LI An-ran, LI Gang 2019, 36 (6):  647-657.  doi: 10.3969/j.issn.1005-3085.2019.06.004 Abstract ( 319 )   PDF (166KB) ( 571 )   Save The Klein-Gordon-Maxwell system has strong physical backgrounds it can describe the ``binary model" between the charged particle matter and the electromagnetic field it produces. According to this model, the particle matter is the solitary wave solution to a nonlinear field equation, and the effect of the electromagnetic field is determined by the coupling of the field equation with the Maxwell equation. In this paper, we use the variational method and critical point theory to study the existence and multiplicity of solutions for a class of Klein-Gordon-Maxwell systems. We first investigate the existence of non-trivial solutions to the above system by using mountain pass lemma, one of the solution is non-negative and the other one is non-positive. Secondly, under some assumptions on the nonlinear term, we establish the existence of infinitely many high energy solutions by using the fountain theorem. Our results generalize the previous conclusions. Related Articles | Metrics

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Existence of Positive Solutions for a Predator-prey Model with Cross-diffusion LV Yang, GUO Gai-hui, YUAN Hai-long, LI Shu-xuan 2019, 36 (6):  658-666.  doi: 10.3969/j.issn.1005-3085.2019.06.005 Abstract ( 277 )   PDF (162KB) ( 482 )   Save The existence of positive solutions to a predator-prey model with cross-diffusion is considered. First, we derive some estimates which are independent of cross-diffusion by the maximum principle; second, the limiting behavior of positive solutions for large cross-diffusion is established; finally, we show the existence of local bifurcation solutions of the limiting system near the semi-trivial solution by the local bifurcation theorem, and we extend the local bifurcation solutions to the global bifurcation solutions by the global bifurcation theorem, and we show that the global bifurcation solutions can extend to infinity as the bifurcation parameter approaches infinity. The results demonstrate that the two species can coexist when the cross-diffusion is large. Related Articles | Metrics

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Uniform Integrability of Sequence of Generalized Functions Described by $K$-quasi Additive Sugeno Integral LI Yan-hong 2019, 36 (6):  667-677.  doi: 10.3969/j.issn.1005-3085.2019.06.006 Abstract ( 279 )   PDF (164KB) ( 431 )   Save $K$-quasi additive Sugeno integral is a new non-additive integral defined by the \mbox{induced} operator, it plays an important role in the generalized integral theory and some practical applications. In order to overcome the inborn deficiency of $K$-quasi additive measure: without additivity, a new non-additive integral model ``$K$-quasi additive Sugeno integral" is introduced. This provides a new way to further study the theory of non-additive integral. On the one hand, on the $K$-quasi additive measure space, the $K$-quasi additive Sugeno integral with the generalized measurable function is defined by the induced operator, and the uniform integrability and uniform boundedness of sequence of generalized functions are discussed by using the analytic representation of the integral. On the other hand, on the $K$-quasi additive measure space, it is proved that the uniform boundedness of a sequence of nonnegative generalized functions contains uniformly integrability, and then a sufficient and necessary condition for the uniformly integrability of the sequence of nonnegative generalized functions is given in the sense of $K$-quasi additive Sugeno integral. Related Articles | Metrics

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The Long-time Behavior of Ratio-dependent Competition Systems WEI Xi, LI Yan-ling, YAN Xiao 2019, 36 (6):  678-692.  doi: 10.3969/j.issn.1005-3085.2019.06.007 Abstract ( 212 )   PDF (145KB) ( 723 )   Save In this paper, we are concerned with the long-time behavior of competition systems between two species with ratio-dependent functional responses subject to the \mbox{homo}geneous Robin boundary condition. First, we establish the existence of positive solutions to these systems by using the fixed point index theory in coin and comparison principle. Second, we discuss the relationships between positive equi-libria and positive solutions of these systems over a large domain. Finally, we study the extinction and permanence of time-dependent positive solutions to these systems and obtain the conditions under which two species can coexist. Related Articles | Metrics

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Stability and Hopf Bifurcation in a Time-delayed Predator-prey System with Stage Structures for Both Predator and Prey ZHU Huan, GAO De-bao 2019, 36 (6):  693-707.  doi: 10.3969/j.issn.1005-3085.2019.06.008 Abstract ( 293 )   PDF (172KB) ( 573 )   Save In nature, population growth often has a process of growing and development. At different age stages, both predators and prey will show different growth characteristics. In addition, the delay has a great influence on the topological structure of differential equation solutions. In many cases, the change of the delay will \mbox{destroy} the stability of the positive equilibrium point and produce Hopf bifurcation. Therefore, this paper takes the growth time from young predator to adult predator as the delay, constructs a time-delayed predator-prey system with stage structure for both predator and prey. Using the persistence theory for infinite-dimensional systems and Hurwitz criterion, the permanent persistence condition of this system and the local stability condition of the system's coexistence equilibrium are given. Choosing the delay as a bifurcation parameter, we derive the existence of the Hopf bifurcation in this system, and then using normal form theory and center manifold arguments, we discuss the direction of the Hopf bifurcation and the stability of period solutions bifurcating from the Hopf bifurcations. Finally, the critical value $\tau_{0n}$ that causes Hopf bifurcation is obtained by choosing the qualified parameters satisfying the theorem conditions, and numerical results are presented to verify the theoretical conclusion. Related Articles | Metrics

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Generating New Super Dynamical Systems in (2+1)-dimensional Space WEI Han-yu, ZHANG Yan, XIA Tie-cheng 2019, 36 (6):  708-720.  doi: 10.3969/j.issn.1005-3085.2019.06.009 Abstract ( 158 )   PDF (123KB) ( 397 )   Save In the article, we make use of the binormial-residue-representation (BRR) to generate (2+1)-dimensional super dynamical systems. By using these systems, a new (2+1)-dimensional super NLS-MKdV hierarchy is deduced, which can be reduced to super nonlinear Schrodinger equation. Especially, two main results are obtained which have important physical applications. One of them is a set of (2+1)-dimensional super integrable couplings, the other one is a (2+1)-dimensional diffusion equation. Furthermore, Super trace identity is used to furnish the super Hamiltonian structures for the new (2+1)-dimensional super integrable system. Related Articles | Metrics

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Improved Partitioned Time Stepping Scheme for the Dual-porosity-Stokes Model HOU Jiang-yong, HU Dan, XU Jin-hu, HE Zheng-kang 2019, 36 (6):  721-732.  doi: 10.3969/j.issn.1005-3085.2019.06.010 Abstract ( 284 )   PDF (512KB) ( 800 )   Save In applications of petroleum reservoir problem, it is very important to study the fluid phases within a complicated porous media coupled with conduit systems. Recently, a dual-porosity-Stokes model is developed to simulate the complicated dual-porosity-conduit system which could be used for realistic problems such as shale/tight oil/gas reservoirs. The new model consists of a dual-porosity model to govern the porous media flow and a Stokes equation to control the free flow and coupled via four interface conditions. Such coupled model is usually hard to solve since it will result into a large and complicated system. In this paper, we propose an improved partitioned time stepping scheme to efficiently and accurately solve the large system caused by the coupled dual-porosity-Stokes model. Related Articles | Metrics