Random linear recursions with dependent coefficients
نویسندگان
چکیده
منابع مشابه
Multivariate linear recursions with Markov-dependent coefficients
We study a linear recursion with random Markov-dependent coefficients. In a “regular variation in, regular variation out” setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established for i.i.d. coefficients.
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For a class of stationary Markov-dependent sequences (ξn, ρn) ∈ R 2, we consider the random linear recursion Sn = ξn + ρnSn−1, n ∈ Z, and show that the distribution tail of its stationary solution has a power law decay. An application to random walks in random environments is discussed. MSC2000: primary 60K15 ; secondary 60K20, 60K37.
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with real-valued random coefficients An and Bn. If the sequence of random pairs (An,Bn)n∈Z is stationary and ergodic, E(log |B0|) < 0, and E(log |A0|+) < ∞, where x+ = max(0, x), then for any initial random value S0, the limit law of Sn is the same as that of the random variable R =A0 +∑∞n=1 A−n∏n−1 i=0 B−i , and it is the unique initial distribution under which (Sn)n≥0 is stationary (cf. [6])....
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ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2010
ISSN: 0167-7152
DOI: 10.1016/j.spl.2010.06.013