Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials
This work establishes exact formulae for the persistence probabilities pk (θ)= P [Y 1⩾ 0,…, Y
k⩾ 0] of an AR (1) sequence Y n= θ Y n− 1+ X n, n= 1, 2,… with parameter θ∈ R﹨(1 2, 2) …
k⩾ 0] of an AR (1) sequence Y n= θ Y n− 1+ X n, n= 1, 2,… with parameter θ∈ R﹨(1 2, 2) …
Persistence exponents in Markov chains
We prove the existence of the persistence exponent $$\log\lambda:=\lim_ {n\to\infty}\frac
{1}{n}\log\mathbb {P} _\mu (X_0\in S,\ldots, X_n\in S) $$ for a class of time homogeneous …
{1}{n}\log\mathbb {P} _\mu (X_0\in S,\ldots, X_n\in S) $$ for a class of time homogeneous …
Persistence exponents via perturbation theory: AR (1)-processes
F Aurzada, M Kettner - Journal of Statistical Physics, 2019 - Springer
Abstract For AR (1)-processes X_n= ρ X_ n-1+ ξ _n X n= ρ X n-1+ ξ n, n ∈ N n∈ N, where ρ
∈ R ρ∈ R and (ξ _i) _ i ∈ N (ξ i) i∈ N is an iid sequence of random variables, we study the …
∈ R ρ∈ R and (ξ _i) _ i ∈ N (ξ i) i∈ N is an iid sequence of random variables, we study the …
[PDF][PDF] Persistence exponents via perturbation theory: autoregressive and moving average processes
M Kettner - 2021 - tuprints.ulb.tu-darmstadt.de
Zusammenfassung In dieser Dissertation werden Persistenz-Wahrscheinlichkeiten von
autoregressiven und Moving-Average-Prozessen studiert. Für einen reellwertigen Prozess …
autoregressiven und Moving-Average-Prozessen studiert. Für einen reellwertigen Prozess …