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On the Approximation of Random Processes by Convolution Processes
Author(s) -
Splettstösser W.
Publication year - 1981
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19810610606
Subject(s) - smoothness , convolution (computer science) , autocorrelation , mathematics , convergence (economics) , weak convergence , function (biology) , process (computing) , order (exchange) , stochastic process , statistical physics , mathematical analysis , computer science , statistics , physics , artificial intelligence , artificial neural network , computer security , finance , evolutionary biology , economics , asset (computer security) , biology , economic growth , operating system
The smoothness in the mean of a weak sense stationary process is closely connected with that of its autocorrelation function. This enables one to prove results on the order of convergence of certain convolution processes to the given random process. On the other hand, it is possible to conclude smoothness properties, in case the order is known.