论文部分内容阅读
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。
The problem of Tf probability distribution for the first time-exceeded Markov process with continuous time series is studied. Let the process increase slightly at any time t, find the internal relations between the transfer probability distribution function of Markov process and the probability distribution of its first overtime by analyzing the relationship of probability changes in the micro-time period, finally get the first overtime Explicit Expressions of Probability Density Functions. Since the harsh mathematical assumptions are not used in the analysis and deduction process, the result of the article is essentially an exact solution. Because of the Markov property of a linear system under the common random white noise excitation, there are many practical methods for converting the reaction into a one-dimensional Markov process when the reaction is not a Markov process. Therefore, the results of this paper are general .