scholarly journals Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes

2021 ◽  
pp. 1-22
Author(s):  
Olha Hopkalo ◽  
Lyudmyla Sakhno
Keyword(s):  
Stochastic Processes ◽  
Sample Paths ◽  
Gaussian Stochastic Processes

scholarly journals Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions

2020 ◽  
pp. 17-24
Author(s):  
O. Hopkalo ◽  
L. Sakhno ◽  
O. Vasylyk
Keyword(s):  
Heat Equation ◽  
Stochastic Processes ◽  
Initial Conditions ◽  
Unbounded Domains ◽  
Stationary Processes ◽  
Sample Paths ◽  
Random Initial Conditions ◽  
Gaussian Stochastic Processes

In this paper, there are studied sample paths properties of stochastic processes representing solutions (in $L_2(\Omega)$ sense) of the heat equation with random initial conditions given by $\varphi$-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded and unbounded domains.

Evaluations of absorption probabilities for the Wiener process on large intervals

1980 ◽  
Vol 17 (02) ◽  
pp. 363-372 ◽  
Author(s):  
C. Park ◽  
F. J. Schuurmann
Keyword(s):  
Stochastic Processes ◽  
Wiener Process ◽  
Standard Wiener Process ◽  
Computationally Efficient ◽  
The Past ◽  
Gaussian Stochastic Processes ◽  
Absorption Probabilities

Let {W(t), 0≦t<∞} be the standard Wiener process. The computation schemes developed in the past are not computationally efficient for the absorption probabilities of the type P{sup0≦t≦T W(t) − f(t) ≧ 0} when either T is large or f(0) > 0 is small. This paper gives an efficient and accurate algorithm to compute such probabilities, and some applications to other Gaussian stochastic processes are discussed.

Tolerant control for non-Gaussian stochastic processes with unknown faults via two-step fuzzy modeling

2018 ◽  
Vol 95 (4) ◽  
pp. 2703-2716 ◽  
Author(s):  
Yang Yi ◽  
Liren Shao ◽  
Xiangxiang Fan ◽  
Tianping Zhang
Keyword(s):  
Stochastic Processes ◽  
Fuzzy Modeling ◽  
Non Gaussian ◽  
Gaussian Stochastic Processes

On the modeling of linear system input stochastic processes with given accuracy and reliability

2018 ◽  
Vol 24 (2) ◽  
pp. 129-137
Author(s):  
Iryna Rozora ◽  
Mariia Lyzhechko
Keyword(s):  
Banach Space ◽  
Stochastic Process ◽  
Linear System ◽  
Stochastic Processes ◽  
Impulse Response Function ◽  
Output Process ◽  
Gaussian Stochastic Process ◽  
System Input ◽  
Time Invariant ◽  
Gaussian Stochastic Processes

AbstractThe paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space{C([0,1])}, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

Simulation of Gaussian stochastic processes

2003 ◽  
Vol 11 (3) ◽  
Author(s):  
Yuri Kozachenko ◽  
Iryna Rozora
Keyword(s):  
Banach Space ◽  
Stochastic Processes ◽  
Gaussian Processes ◽  
Gaussian Stochastic Processes

In this paper the Gaussian stochastic processes, represented in the form of series, are considered. The approximating models of the Gaussian processes with given reliability and accuracy in Banach space C

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