Martin Kolb, Paderborn: Persistence of one-dimensional AR(1)-sequence (Oberseminar Mathematische Stochastik)
Wednesday, 06.06.2018 17:00 im Raum SRZ 205
Motivated by previous work of Aurzada, Mukherjee and Zeitouni on persistence exponents
of Markov chains and in particular autoregressive processes we consider the tail behaviour of the
stopping time \(T_0 = min\{n \ge 1 : X_n \le 0\}\) for a class of one-dimensional autoregressive processes
\((X_n)\). We discuss existing general analytic/probabilistic approaches to this and related problems
and propose a new one, which is based on a renewal-type decomposition for the moment generating
function of \(T_0\) and on the analytic Fredholm alternative. Using this method, we show that \(P_x(T_0 = n) \sim
V (x)R_0^n\) for some \(0 < R_0 < 1\). Furthermore we are able to prove convergence towards
quasistationarity in our situation.
(Joint work with G. Hinrichs and V. Wachtel)
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Angelegt am 27.04.2018 von Anita Kollwitz
Geändert am 30.05.2018 von Anita Kollwitz
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