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Limiting process of absorbing markov chains

Frontiers of Mathematics in China 2014年第4期9卷 753-759页

作者： Jinwen CHEN Department of Mathematical Sciences Tsinghua University Beijing 100084 China

We outline an approach to investigate the limiting law of an absorbing markov chain conditional on having not been absorbed for long time. The main idea is to employ Donsker-Varadhan＇s entropy functional which is typically used as the large deviation rate function for markov processes. This approach provides an interpretation for a certain quasi-ergodicity

关键词： absorbing markov chain large deviation principal eigenvalue,quasi-stationary distribution decay parameter

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Application Research on Two-Layer Threat Prediction Model Based on Event Graph

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Computers, Materials & Continua 2023年第12期77卷 3993-4023页

作者： Shuqin Zhang Xinyu Su Yunfei Han Tianhui Du Peiyu Shi School of Computer Science Zhongyuan University of TechnologyZhengzhouHEN037China

Advanced Persistent Threat(APT)is now the most common network ***,the existing threat analysis models cannot simultaneously predict the macro-development trend and micro-propagation path of APT *** cannot provide rapid and accurate early warning and decision responses to the present system state because they are inadequate at deducing the risk evolution rules of network *** address the above problems,firstly,this paper constructs the multi-source threat element analysis ontology(MTEAO)by integrating multi-source network security knowledge ***,based on MTEAO,we propose a two-layer threat prediction model(TL-TPM)that combines the knowledge graph and the event *** macro-layer of TL-TPM is based on the knowledge graph to derive the propagation path of threats among devices and to correlate threat elements for threat warning and decision-making;The micro-layer ingeniously maps the attack graph onto the event graph and derives the evolution path of attack techniques based on the event graph to improve the explainability of the evolution of threat *** experiment’s results demonstrate that TL-TPM can completely depict the threat development trend,and the early warning results are more precise and scientific,offering knowledge and guidance for active defense.

关键词： Knowledge graph multi-source data fusion network security threat modeling event graph absorbing markov chain threat propagation path

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Non-saturated throughput analysis of IEEE 802.11-based cognitive radio networks

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The Journal of China Universities of Posts and Telecommunications 2012年第6期19卷 6-13页

作者： ZHAO Yuan JIN Shun-fu TIAN Nai-shuo College of Information Science and Engineering Yanshan University College of Science Yanshan University

Technology of cognitive radio networks has emerged as an effective method to enhance the utilization of the radio spectrum where the primary users have priority to use the spectrum, and the secondary users try to exploit the spectrum unoccupied by the primary users. In this paper, considering the non-saturated condition, the performance analysis for the IEEE 802.11-based cognitive radio networks is presented with single-channel and multi-channel, respectively. For the single-channel case, an absorbing markov chain model describing the system transitions is constructed, and one-step transition probability matrix of the markov chain is given. By using the method of probability generating function, the non-saturated throughput of the secondary users is obtained. For the multi-channel case, taking into account the negotiation-based sensing policy, the mean number of unused channels perceived by the second users is given, and then the non-saturated aggregate throughput of the secondary users is derived. Finally, numerical examples are provided to show the influences of the non-saturated degree, the number of the secondary users and the channel utilization of the primary users on the performance measures for the non-saturated throughput with single-channel and the non-saturated aggregate throughput with multi-channel.

关键词： cognitive radio networks IEEE 802.11 non-saturated throughput absorbing markov chain probability generating function

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ON THE SPH-DISTRIBUTION CLASS

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Acta Mathematica Scientia 2005年第2期25卷 201-214页

作者：史定华郭进利刘黎明 Department of Mathematics Shanghai University Shanghai 200436 China College of Management University of Shanghai for Science and Technology Shanghai 200093 China Department of Industrial Engineering and Engineering Management The Hong Kong University of Science and Technology Hong Kong China

Following up Neuts' idea, the SPH-distribution class associated with bounded Q matrices for infinite markov chains is denned. The main result in this paper is to characterize the SPH class through the derivatives of the distribution functions. Based on the characterization theorem, closure properties, the expansion, uniform approximation, and the matrix representations of the SPH class are also discussed by the derivatives of the distribution functions at origin.

关键词： Phase type distribution absorbing markov chain operator theory SPHdistribution properties

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