Convergence of the integration of the stationary weakly correlated process
Received:July 25, 1984  
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Lin Zhengyan Hangzhou University 
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Abstract:
      Lei g(x,ω) be a stationary weakly conelated process, G(t, x) be the Green's function and G(x) be a function with a smooth one-order derivative. Define stochastic processes ξ(t,ω)=∫01G(t,x)g(x,ω)dx (0≤t≤1) and η(t,ω)=∫0tG(x)g(x,ω)dx (0≤t≤T) In this paper we give the strong approximations of random variables ξ(t) and η(t) to normal variables, and also give a weakly in variance principle for process η(·).
Citation:
DOI:10.3770/j.issn:1000-341X.1987.04.031
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