24 citations · 80 across the 13 of their papers we have counts for
5 papers · 1 filter
Affine stochastic equation with triangular matrices
Ewa Damek, Jacek Zienkiewicz
We study solution X of the stochastic equation X = AX +B, where A is a random matrix and B,X are random vectors, the law of (A,B) is given and X is independent of (A,B). The equati…
Pointwise estimates for first passage times of perpetuity sequences
Dariusz Buraczewski, Ewa Damek, Jacek Zienkiewicz
We consider first passage times for the perpetuity sequence where are i.i.d. ran…
Large deviation estimates for exceedance times of perpetuity sequences and their dual processes
Dariusz Buraczewski, Jeffrey F. Collamore, Ewa Damek +1
In a variety of problems in pure and applied probability, it is of relevant to study the large exceedance probabilities of the perpetuity sequence $Y_n := B_1 + A_1 B_2 + \cdots +…
Large deviations for solutions to stochastic recurrence equations under Kesten's condition
D. Buraczewski, E. Damek, T. Mikosch +1
In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (19…
Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices
Ewa Damek, Sebastian Mentemeier, Mariusz Mirek +1
Given a sequence of i.i.d.\ random variables with generic copy , we consider the random difference equation (RDE) $$ R_{n}…