Chinese Journal of Theoretical and Applied Mechanics ›› 2019, Vol. 51 ›› Issue (5): 14371447.DOI: 10.6052/0459187919104
• Dynamics, Vibration and Control • Previous Articles Next Articles
Received:
20190425
Online:
20190918
Published:
20190930
Contact:
Chen Jianbing
CLC Number:
Chen Jianbing, Lü Mengze. A NEW METHOD FOR THE PROBABILITY DENSITY OF MAXIMUM ABSOLUTE VALUE OF A MARKOV PROCESS^{1)}[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 14371447.
[1]  Arrechi FT . Transition Phenomena in Nonlinear Optics. Berlin: Springer, 1981 
[2]  Bras RL . Hydrology: An Introduction to Hydrological Science. Reading: AddisonWesley, 1990 
[3]  胡岗 . 随机力与非线性系统. 上海: 上海科技教育出版社, 1994 
( Hu Gang. Stochastic Forces and Nonlinear Systems. Shanghai: Shanghai Scientific and Technological Education Publishing House, 1994 (in Chinese))  
[4]  øksendal B. Stochastic Differential Equations. 5th Ed. Berlin: SpringerVerlag, 1998 
[5]  Hull JC. Option , Futures, Other Derivatives. 4th Ed. Upper Saddle River: PrenticeHall, 2000 
[6]  Li J, Chen JB . Stochastic Dynamics of Structure. Singapore: John Wiley & Sons (Asia) Pte Ltd, 2009 
[7]  苏成, 徐瑞 . 非平稳随机激励下结构体系动力可靠度时域解法. 力学学报, 2010,42(3):512520 
( Su Cheng, Xu Rui . Timedomain method for dynamic reliability of structural systems subjected to nonstationary random excitations. Chinese Journal of Theoretical and Applied Mechanics, 2010,42(3):512520 (in Chinese))  
[8]  Fisher RA, Tippett LHC . Limiting forms of the frequency distribution of the largest and smallest member of a sample. Mathematical Proceedings of the Cambridge Philosophical Society, 1928,24(2):180190 
[9]  Gumbel EJ. Statistics of Extremes. New York: Columbia University Press, 1958 
[10]  Coles S . An Introduction to Statistical Modeling of Extreme Values. Springer, 2001 
[11]  Powell A . On the fatigue failure of structures due to vibration excited by random pressure fields. The Journal of the Acoustical Society of America, 1958,30(2):11301135 
[12]  Dudley RM. Real Analysis and Probability. Cambridge: The Press Syndicate of the University of Cambridge, 1989 
[13]  Klebaner FC. Introduction to Stochastic Calculus with Application. 2nd Ed. London: Imperial College Press, 2005 
[14]  Redner S. A Guide to FirstPassage Processes. Cambridge: Cambridge University Press, 2001 
[15]  陈建兵, 李杰 . 非线性随机结构动力可靠度的密度演化方法. 力学学报, 2004,36(2):196201 
( Chen Jianbing, Li Jie . The probability density evolution method for dynamic reliability assessment of nonlinear stochastic structures. Chinese Journal of Theoretical and Applied Mechanics, 2004,36(2):196201 (in Chinese))  
[16]  Monili A, Talkner P, Katul GG , et al. First passage time statistics of Brownian motion with purely time dependent drift and diffusion. Physica A  Statistical Mechanics & Its Applications, 2011,390:18411852 
[17]  Kou S, Zhong H . Firstpassage times of twodimensional Brownian motion. Advanced Applied Probability, 2016,48:10451060 
[18]  Li J, Chen JB . The principle of preservation of probability and the generalized density evolution equation. Structural Safety, 2008,30:6577 
[19]  陈建兵, 张圣涵 . 非均布随机参数结构非线性响应的概率密度演化. 力学学报, 2014,46(1):136144 
( Chen Jianbing, Zhang Shenghan . Probability density evolution analysis of nonlinear response of structures with nonuniform random parameters. Chinese Journal of Theoretical and Applied Mechanics, 2014,46(1):136144 (in Chinese))  
[20]  Chen JB, Li J . The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters. Structural Safety, 2007,29:7793 
[21]  Mannella R, Palleschi V . Fast and precise algorithm for computer simulation of stochastic differential equations. Physical Review A, 1989,40(6):33813386 
[22]  Honeycutt RL . Stochastic RungeKutta algorithms. I. White noise. Physical Review A, 1992,45(2):600603 
[23]  Honeycutt RL . Stochastic RungeKutta algorithms. II. Colored noise. Physical Review A, 1992,45(2):604610 
[24]  Higham DJ . An algorithmic introduction to numerical simulation of stochastic differential equations. Society for Industrial and Applied Mathematics, 2001,43(3):525546 
[25]  朱位秋. 随机振动. 北京:科学出版社, 1992 
( Zhu Weiqiu. Random Vibration. Beijing: Science Press, 2003)  
[26]  Gardiner CW . Handbook of Stochastic Methods for Physics. 2nd Ed. Berlin: SpringerVerlag, 1985 
[27]  徐伟 . 非线性随机动力学的若干数值方法及应用. 北京: 科学出版社, 2013 
( Xu Wei. Numerical Analysis Methods for Stochastic Dynamical System. Beijing: Science Press, 2013 (in Chinese))  
[28]  Risken H . The FokkerPlanck Equation. 2nd Ed. Berlin: SpringerVerlag, 1989 
[29]  Chen JB, Lyu MZ . A new approach for the timevariant probability density function of the maximum value of a Markov process. Journal of Computational Physics, 2019 ( under review) 
[30]  Lyu MZ, Chen JB, Pirrotta A . A novel method based on augmented Markov vector process for the timevariant extreme value distribution of stochastic dynamical systems enforced by Poisson white noise. Communications in Nonlinear Science and Numerical Simulation, 2019 ( accepted) 
[31]  Er GK . Exponential closure method for some randomly excited nonlinear systems. International Journal of NonLinear Mechanics, 2000,35:6978 
[32]  朱位秋 . 非线性随机动力学与控制Hamilton理论体系框架. 北京: 科学出版社, 2003 
( Zhu Weiqiu. Nonlinear Stochastic Dynamics and ControlHamiltonian Formulation. Beijing: Science Press, 2003 (in Chinese))  
[33]  Chen JB, Yuan SR . Dimension Reduction of the FPK Equation via an Equivalence of Probability Flux for Additively Excited Systems. Journal of Engineering Mechanics, 2014,140(11):04014088 
[34]  Chen JB, Rui ZM . Dimensionreduced FPK equation for additive whitenoise excited nonlinear structures. Probabilistic Engineering Mechanics, 2018,53:113 
[35]  芮珍梅, 陈建兵 . 加性非平稳激励下结构速度响应的FPK方程降维. 力学学报, 2019,51(3):922931 
( Rui Zhenmei, Chen Jianbing . Dimension reduction of FPK equation for velocity response analysis of structures subjected to additive nonstationary excitations. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):922931 (in Chinese)) 
[1]  Cheng Su Rui Xu. Timedomain method for dynamic reliability of structural systems subjected to nonstationary random excitations [J]. Chinese Journal of Theoretical and Applied Mechani, 2010, 42(3): 512520. 
[2]  ,,,. Dynamic reliability analysis of stochastic truss structures under stationary random excitation [J]. Chinese Journal of Theoretical and Applied Mechani, 2004, 36(2): 00. 
[3]  ,. The probability density evolution method for dynamic reliability assessment of nonlinear stochastic structures [J]. Chinese Journal of Theoretical and Applied Mechani, 2004, 36(2): 00. 
[4]  . THE PROBABILITY DENSITY FUNCTIONS OF THE STATIONARY RESPONSE OF CERTAIN CLASSES OF NONLINEAR SYSTEMS TO STOCHASTIC EXCITATION [J]. Chinese Journal of Theoretical and Applied Mechani, 1991, 23(1): 92102. 
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