Gaussian Stochastic Processes: Gaussian Fields and Their Realizations

2021 ◽  
pp. 85-159
Keyword(s):  
Stochastic Processes ◽  
Gaussian Fields ◽  
Gaussian Stochastic Processes

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

The horizon problem for random surfaces

1991 ◽  
Vol 109 (1) ◽  
pp. 211-219 ◽  
Author(s):  
K. J. Falconer
Keyword(s):  
Computer Simulation ◽  
Stochastic Processes ◽  
Random Field ◽  
Random Fields ◽  
Sample Function ◽  
Gaussian Fields ◽  
Random Surfaces ◽  
Horizon Problem ◽  
Typical Sample

Computer simulation of landscapes and skylines has recently attracted a great deal of interest: see [6, 7]. Specification of a ‘landscape’ requires a function f: D → ℝ on a subset D of ℝ2, selected so that the apparent irregularity and randomness of the surface {(t,f(t)): t ∈ D} corresponds to what might be observed in nature. It is natural to look to random fields (that is, stochastic processes in two variables), and in particular to Gaussian fields, for functions with such properties. Even when an appropriate random field has been selected, determination of a typical sample function is far from easy [7].

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