Sample Function Analysis of Continuous Parameter Stochastic Processes

1975 ◽  
pp. 161-209
Author(s):  
ROBERT B. ASH ◽  
MELVIN F. GARDNER
Keyword(s):  
Stochastic Processes ◽  
Function Analysis ◽  
Sample Function ◽  
Continuous Parameter

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].

Machine/Process Parameter Monitoring Using Sample Function Analysis

1996 ◽  
Vol 8 (4) ◽  
pp. 553-563
Author(s):  
Narimants Salenieks ◽  
Agris Aizpurietis ◽  
Edgars Balcers
Keyword(s):  
Function Analysis ◽  
Process Parameter ◽  
Sample Function ◽  
Machine Process ◽  
Parameter Monitoring
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