Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Damek, Ewa"'
Autor:
Damek, Ewa, Mentemeier, Sebastian
In recent works on the theory of machine learning, it has been observed that heavy tail properties of Stochastic Gradient Descent (SGD) can be studied in the probabilistic framework of stochastic recursions. In particular, G\"{u}rb\"{u}zbalaban et al
Externí odkaz:
http://arxiv.org/abs/2403.13868
We consider a strictly stationary random field on the two-dimensional integer lattice with regularly varying marginal and finite-dimensional distributions. Exploiting the regular variation, we define the spatial extremogram which takes into account o
Externí odkaz:
http://arxiv.org/abs/2211.03260
Autor:
Damek, Ewa, Matsui, Muneya
We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions ${\bf W} =(W_1,W_2)$. Recently it has been observed that $W_1,W_2$ may exhibit regularly varyin
Externí odkaz:
http://arxiv.org/abs/2110.04546
Autor:
Damek, Ewa
Multivariate process satisfying affine stochastic recurrence equation with generic diagonal matrices is considered. We prove that the stationary solution is regularly varying. The results are applicable to diagonal autoregressive models.
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Externí odkaz:
http://arxiv.org/abs/2106.11243
Autor:
Buraczewski, Dariusz, Damek, Ewa
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus on the su
Externí odkaz:
http://arxiv.org/abs/2007.00443
Autor:
Damek, Ewa, Kołodziejek, Bartosz
Publikováno v:
Electron. Commun. Probab. 23 (2018), str. 1 - 13
We study tails of the supremum of a perturbed random walk under regime which was not yet considered in the literature. Our approach is based on a new renewal theorem, which is of independent interest. We obtain first and second order asymptotics of t
Externí odkaz:
http://arxiv.org/abs/1812.04496
Publikováno v:
In Stochastic Processes and their Applications January 2023 155:232-267
Autor:
Damek, Ewa, Zienkiewicz, Jacek
Publikováno v:
Journal of Difference Equations and Applications, 2018
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 equation is meant in law, the matrix A is 2x2 upper triangular, A_{11}=A_{22
Externí odkaz:
http://arxiv.org/abs/1806.08985
We consider a supercritical branching process $Z_n$ in a stationary and ergodic random environment $\xi =(\xi_n)_{n\ge0}$. Due to the martingale convergence theorem, it is known that the normalized population size $W_n=Z_n/ (\mathbb E (Z_n|\xi ))$ co
Externí odkaz:
http://arxiv.org/abs/1806.04902
Autor:
Damek, Ewa, Mentemeier, Sebastian
Let $X$ be a $\mathbb{C}$-valued random variable with the property that $$X \ \text{ has the same law as }\ \sum_{j\ge1} T_j X_j$$ where $X_j$ are i.i.d.\ copies of $X$, which are independent of the (given) $\mathbb{C}$-valued random variables $ (T_j
Externí odkaz:
http://arxiv.org/abs/1804.02209