Random Processes and Stochastic Systems

2003 ◽  
pp. 56-113
Keyword(s):  
Stochastic Systems ◽  
Random Processes

Statistics of an Appealing Class of Random Processes

2021 ◽  
pp. 260-276
Author(s):  
Shaival Hemant Nagarsheth ◽  
Shambhu Nath Sharma
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Correction Term ◽  
Random Processes ◽  
Random Perturbations ◽  
White Noise Process ◽  
Coloured Noise ◽  
Diffusion Operator ◽  
Noise Process ◽  
Special Cases

The white noise process, the Ornstein-Uhlenbeck process, and coloured noise process are salient noise processes to model the effect of random perturbations. In this chapter, the statistical properties, the master's equations for the Brownian noise process, coloured noise process, and the OU process are summarized. The results associated with the white noise process would be derived as the special cases of the Brownian and the OU noise processes. This chapter also formalizes stochastic differential rules for the Brownian motion and the OU process-driven vector stochastic differential systems in detail. Moreover, the master equations, especially for the coloured noise-driven stochastic differential system as well as the OU noise process-driven, are recast in the operator form involving the drift and modified diffusion operators involving an additional correction term to the standard diffusion operator. The results summarized in this chapter will be useful for modelling a random walk in stochastic systems.

scholarly journals POWER LAWS ARE LOGARITHMIC BOLTZMANN LAWS

1996 ◽  
Vol 07 (04) ◽  
pp. 595-601 ◽  
Author(s):  
MOSHE LEVY ◽  
SORIN SOLOMON
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Degrees Of Freedom ◽  
Stochastic Systems ◽  
Power Laws ◽  
Random Processes ◽  
Fine Tuning ◽  
Power Law Distribution ◽  
Natural Origin ◽  
Dispersion Law

Multiplicative random processes in (not necessarily equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.

Methods for modeling and estimating random variables and processes

2020 ◽  
Author(s):  
Evgeniy Butyrskiy
Keyword(s):  
Mathematical Modeling ◽  
Research Methods ◽  
Learning Process ◽  
Stochastic Systems ◽  
Random Processes ◽  
Theory And Practice ◽  
State University ◽  
Mathematical Research ◽  
Wide Range ◽  
Random Events

The monograph introduces the basics of theory and practice of mathematical research methods of stochastic systems and processes. It examines the models, methods of describing and forming random events, values and processes, as well as methods of their optimal and suboptimal assessment. The monograph can be useful for a wide range of specialists in various fields of expertise in mathematical and statistical modeling in their research, and can also be used in the learning process to conduct both classroom, and independent theoretical and practical classes with students and masters of St. Petersburg State University engaged in the program «Mathematical modeling» and «Optimal and suboptimal assessment of random processes and systems».

Almost-Sure Stability of Some Linear Stochastic Systems

1989 ◽  
Vol 56 (1) ◽  
pp. 175-178 ◽  
Author(s):  
S. T. Ariaratnam ◽  
B. L. Ly
Keyword(s):  
Stochastic Systems ◽  
Stability Boundary ◽  
Quadratic Function ◽  
Random Processes ◽  
Almost Sure Stability ◽  
Special Cases ◽  
Linear Stochastic Systems ◽  
The Matrix ◽  
The Stability ◽  
Second Order Systems

The almost-sure stability of linear second-order systems which are parametrically excited by ergodic, “nonwhite,” random processes is studied by an extension of the method of Infante. In this approach, a positive-definite quadratic function of the form V = x′Px is assumed and a family of stability boundaries depending on the elements of the matrix P is obtained. An envelope of these boundaries is then solved for by optimizing the stability boundary with respect to the elements of P. It is found that the optimum matrix P in general depends not only on the system constants but also on the excitation intensities. This approach is, in principle, applicable to study systems involving two or more random processes. The results reported in previous investigations are obtained as special cases of the present study.

The psychophysics of random processes

1976 ◽  
Author(s):  
Renwick E. Curry ◽  
T. Govindaraj
Keyword(s):  
Random Processes
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