STOCHASTIC ASYMPTOTIC STABILITY AND APPROXIMATION OF THE RANDOM SOLUTION OF A STOCHASTIC DISCRETE FREDHOLM SYSTEM

Abstract

A stochastic discrete Fredholm system in the form xn(ω) = hn(ω) + ∞Σj=1 Cn,j(ω)ƒj(xj(ω)), n = 1,2,…, is studied, where ω ∈ Ω, the supporting set of a complete probability measure space (Ω,A,P). A random solution of the discrete system is defined to be a discrete parameter second order stochastic process xn(ω) that satisfies the equation almost surely. The stochastic geometric stability of xn(ω) is defined, and conditions are given under which the random solution has this property. A finite system which approximates the infinite system is given, and it is shown that under certain conditions the unique random solution of the approximating system converges to the unique random solution of the infinite system.

Citation

PADGETT, W.J. and TSOKOS, C.P. (1973), "STOCHASTIC ASYMPTOTIC STABILITY AND APPROXIMATION OF THE RANDOM SOLUTION OF A STOCHASTIC DISCRETE FREDHOLM SYSTEM", Kybernetes, Vol. 2 No. 4, pp. 239-251. https://doi.org/10.1108/eb005344