【摘要】 对时间连续状态连续的Markov过程的首次超越时间Tf概率分布问题进行了研究。令过程在任意时刻t发生微增量?t,通过分析?t微时段内的概率变化关系寻求Markov过程的转移概率分布函数与其首超时间概率分布之间的内在联系,最终得到了首超时间概率密度函数的解析显式表达式。由于在分析推导过程中没有采用苛刻的数学假定,因此该文结果在本质上属精确解。由于在常见随机荷载白噪声激励下线性体系的反应具有Markov性,而对于反应不是Markov过程的情形有不少实用的方法可将其转化为一维Markov过程,因此该文的研究结果具有一般性。更多还原

【Abstract】 The paper studies the probability distribution of the first-passage time Tf of Markov process,whose times and states are both continuous.Considering minute time increment at time t,the paper examines the probability variation in the minute time-interval to find the internal relation between transition probability distribution function and first-passage times probability distribution.Finally the explicit expression of probability density function of first-passage time is obtained.The responses of linear system have Markov property under common random loads-flat noise,and the non-Markov responses process can be converted to one-dimensional Markov process by quite a few existing practical methods,so this study has generality.更多还原