Author(s):  
Bogdan-Vasile Cioruța

The purpose of this study is to familiarize the reader with the diversity of concepts (notions) and stages of development specific to Probability Theory, with the definition and characterization of variables, vectors and random processes, respectively with the most important elements that give random processes. Among these we mention the distribution function, the probability density function, the statistical moments of a random process, the temporal averages, and respectively the correlation (and intercorrelation) of a random signal (process). Also, the implications of random processes in the study of dynamical systems are reviewed, as well as a series of applications specific to the analysis of dynamic behavior.


1998 ◽  
pp. 39-67
Author(s):  
Simon J. Godsill ◽  
Peter J. W. Rayner

2014 ◽  
Vol 607 ◽  
pp. 817-820 ◽  
Author(s):  
Aleksandr Vasilyevich Pitukhin ◽  
Igor Skobtsov

The development of new catastrophe theory methods, coupled with probability theory is opening new possibilities to estimate the reliability measures. A brief review of the cusp catastrophe is presented in the introduction. The second part is devoted to probability approach. Manage variables are viewed as stationary random processes (functions) and a problem of overshoot of random function is formulated. Mean number of zero crossings by Gaussian random stationary process is evaluated; analytical equations to estimate the reliability function are obtained.


2019 ◽  
pp. 37-88
Author(s):  
Marcelo S. Alencar ◽  
Valdemar C. da Rocha

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