刘源远

研究方向：

马氏过程的遍历性；排队论及排队网络

主讲课程/工作岗位：

概率论与数理统计，数学分析，实变函数，泛函分析

1.主持中南大学‘升华育英计划’科研启动基金项目（2010.11-2015.11 ）

2. 主持高校基本科研业务费重点项目：马氏过程与随机控制（2010.01-2011.12 ）

3. 主持国家自然科学基金青年基金项目: 马氏过程的遍历性和有限排队丢失概率的渐近性(2010.01-2012.12 )

4. 主持教育部留学回国基金项目: 有限排队丢失概率的渐近性及二维排队过程的稳定性 (2010.01-2012.12 )

5.主持湖南省骨干青年教师基金 (2010.01-2012.12 )

已完成项目：

1. 排队过程的瞬时分布、遍历性及其应用。（国家自然科学基金，参与）

2. 马氏骨架过程及其在排队论、运筹学和可靠性理论中的应用。（高校博士点基金，参与）

3. 马氏链遍历速度的研究 。 （中南大学研究生教育创新工程， 主持）

4. Introductory Functional Analysis with Applications （中南大学研究生教育创新工程教改项目， 主持）

已发表论文与专著：

• [1] Yuanyuan Liu, Yang Li. V-uniform ergodicity for fluid queues [J]. Applied Mathematics-A Journal of Chinese Universit, 2019, 34(1): 82-91
• [2] Yuanyuan Liu, Wendi Li. Exact tail asymptotics for fluid models driven by M/M/c queue [J]. Queueing Systems, 2019,
• [3] Yuanyuan Liu, Wendi Li. Error bounds for augmented truncation approximations of Markov chains via the perturbation method [J]. Advances in Applied Probability, 2018, 50(2): 645-669
• [4] Yuanyuan Liu, Pengfei Wang, Yiqiang Zhao. The variance constant for continuous-time level dependent quasi-birth-and-death processes Stochastic Models, 2018, 34(1): 25-44
• [5] Yuanyuan Liu, Yanhong Song. Integral-type functionals of first hitting times for continuous-time Markov chains Frontiers of Mathematics in China, 2018, 13(3): 619-632
• [6] Yuanyuan Liu, Wendi Li, Hiroyuki Masuyama. Error bounds for augmented truncation approximations of continuous-time Markov chains [J]. Operations Research Letters, 46(9): 1-6
• [7] Shuxia Jiang, Yuanyuan Liu, Yingchun Tang. A unified perturbation analysis framework for countable Markov chains Linear Algebra and Its Applications, 2017, 529(15): 413-440
• [8] Shuxia Jiang, Guy Latouche, Yuanyuan Liu. Wavelet transform for quasi-birth-death processes with a continous phase set Applied Mathematics and Computation, 2015, 252(1): 354-376
• [9] Yuanyuan Liu. Perturbation analysis for continous-time Markov chains [J]. 2015, 58, No. 12: 2633–2642: SCIENCE CHINA Mathematics, 2015, 58(12): 2633–2642PDF
• [10] Yuanyuan Liu, Yingchun Tang, Yiqiang Zhao. Censoring technique and numerical computations of invariant distribution for continuous-time Markov chains
• [11] Shuxia Jiang and Yuanyuan Liu. Injector waveform analysis and engine fault diagnosis based on frequency space subdivision in wavelet transform
• [12] Shuxia Jiang, Yuanyuan Liu and Shuai Yao. Poisson equation for discrete-time single-birth processes [J]. Statistics and Probability Letters, 2014, 85: 78--83
• [13] Yuanyuan Liu, Yuhui Zhang. Central limit theorems for ergodic ontinuous -time Markov chains with applications to single birth processes [J]. Front. Math. China, 2015, 10(4): 933–947
• [14] Yuanyuan Liu, Pengfei Wang, Yanmin Xie. Deviation matrix and asymptotic variance for GI/M/1-type Markov chains Frontiers of Mathematics in China, 2014, 9(4): 863-880
• [15] Dendievel Sarah，Latouche Guy，Liu Yuanyuan. Poisson's equation for discrete-time quasi-birth-and-death processes Performance Evaluation, 2013, 70(9): 564-577
• [16] Shuxia Jiang, Yiping Luo and Yuanyuan Liu. Method for engine waveform analysis and fault diagnosis based on SFB and HHT Advances in Adaptive Data Analysis, 5(4):
• [17] Yuanyuan Liu, Yiqiang Zhao. Asymptotic behavior of the loss probability for an M/G/1/N queue with vacations [J]. Applied Mathematical Modelling, 2013, 37(4): 1768-1780
• [18] Yuanyuan Liu. Perturbation bounds for the stationary distributions of Markov chains [J]. SIAM Journal on Matrix Analysis and Applications, 2012, 33(4): 1057-1074
• [19] Shuxia Jiang, Yuanyuan Liu and Hong Zhang. SFB selection method and its application in engine waveform analysis and fault diagnosis [C]. ICWAPR 2012, 296-301, 2011,
• [20] Yuanyuan Liu. Additive functionals for Discrete-time Markov chains with applications to birth-death processes Journal of Applied Probability, 2011, 48(4): 925-937