Analysis of a stochastic difference equation: exit times and invariant distributions

• Autorzy: Högnäs G. , Jung B.
• Języki publikacji: EN

Abstrakty

EN

The mean return time of a discrete Markov chain to a point x is the reciprocal of the invariant probability π(x). We revisit this classical theme to investigate certain exit times for stochastic difference equations of autoregressive type. More specifically, we will discuss the asymptotics, as 0, of the first time that the n-dimensional process ...[wzór] (where ξ1, ξ2, . . . is a sequence of i.i.d. random n-vectors) leaves a given neighborhood of the fixed point of the contraction f.

Słowa kluczowe

EN

return times; autoregressive processes; recurrence; multivariate normal

PL

punkt stały; analiza stochastyczna; równanie różnicowe

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 44
• Strony: 69--74
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Högnäs G.

autor

Jung B.

• Abo Akademi University Department of Mathematics FIN-20500 Finland,

Bibliografia

• [1] Cogburn R., A uniform theory for sums of Markov chain transition probabilities, Ann. Probab., 3(2)(1975), 191-214.
• [2] Kac M., On the notion of recurrence in discrete stochastic processes, Bull. Amer. Math. Soc., 53(1947), 1002-1010.
• [3] Klebaner F., Liptser R., Large deviations for past-dependent recursions, Probl. Inf. Transm., 32(1996), 23-34. (Corrected version 2006).
• [4] Meyn S.P., Tweedie R.L., Markov Chains and Stochastic Stability, Springer- Verlag, 1993.
• [5] Ruths B., Exit times for past-dependent systems, Surveys of Applied and Industrial Mathematics (Obozrenie prikladnoy i promyshlennoy matematiki), 15(1)(2008), 25-30.