Abstract: This paper tries to utilize the methods of stochastic analysis and matrix analysis to research the existential problem of price series.By using the means of time series analysis, the input-output,Markov processes and the modern matrix analysis,the limiting problem of price balance and vibration in stochastic economic environment has been researched,and surprising conclusions obtained are as following:the probability that the economic collapse time is equal∞is 0.

Key words:  input-output coefficient matrix, economic collapse time, maximum eigne value, random perturbation, Markov process