摘要
N.Singh和M.S.Peiris研究了非平稳自回归滑动和过程,组出了解的存在定理,以及有关的一些性质,本工作举例说明,他门用以表示解的级数可以不收敛。
A counter example to N. Singh and M. S. Peiris' Theorem 2. 1 (in Stochastic Processes and their Applications 24 (1987) 151 - 155) is given as follows. Take Φt (x) = 1 -( - 1)'(2x)/ω+(x2)/(ω2) with fixed ω(1<ω<2). Then it is proved by Math. Induction that g(t,s),the solution of the difference eqution with inertiaconditions g(s-1,s) = 0, g(δ,δ)=1, verifies g(s+t,s)≥(2/ω)'. Take Am= {22m-1k;k odd integer} forpossitive integer m and Am= (2-2mk;k odd integer} for nonpoesitive integer m,Am = (s;s∈Am,g(m,s)forAm respctively. Take Qt(x) = 1 + θ1tx, thenfor and so for any fixed t,X'the solution of the nonstationary ARMA eqution Φt(B) Xt = Qt(B)et, never converges in quadratic mean provided that Bet2 is independent of t.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
1992年第1期12-14,共3页
Journal of Xiamen University：Natural Science
基金
福建省自然科学基金
