24 citations · 80 across the 13 of their papers we have counts for
19 papers
Whittle estimation based on the extremal spectral density of a heavy-tailed random field
Ewa Damek, Thomas Mikosch, Yuwei Zhao +1
We consider a strictly stationary random field on the two-dimensional integer lattice with regularly varying marginal and finite-dimensional distributions. Exploiting the regular v…
On maximal function of discrete rough truncated Hilbert transforms
Maciej Paluszynski, Jacek Zienkiewicz
We prove the weak type (1,1) estimate for maximal function of the truncated rough Hilbert transform considered in [9] and [10]
Dimension independent atomic decoposition for dyadic martingale
Maciej Paluszynski, Jacek Zienkiewicz
We introduce atoms for dyadic atomic for which the equivalence between atomic and maximal function defnitions is dimension independent. We give the sharp, up to fac…
On Inverses of Discrete Rough Hilbert Transforms
Maciej Paluszynski, Jacek Zienkiewicz
We describe the structure of the resolvent of the discrete rough truncated Hilbert transform under the critical exponent. This extends the results obtained in [8].
Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis
Piotr Biler, Jacek Zienkiewicz
We consider the simplest parabolic-elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the blowup of radially symmetric solutions in terms of suitab…
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…
Probabilistic approach to quantum separation effect for Feynman-Kac semigroup
Adam Sikora, Jacek Zienkiewicz
Quantum tunnelling phenomenon allows a particle in Schrödinger mechanics tunnels through a barrier that it classically could not overcome. Even the infinite potentials do not alway…
Weak type (1,1) estimates for inverses of discrete rough singular integral operators
Maciej Paluszynski, Jacek Zienkiewicz
We obtain weak type (1,1) estimates for the inverses of truncated discrete rough Hilbert transform. We include an ex- ample showing that our result is sharp. One of the ingredients…
Large global-in-time solutions to a nonlocal model of chemotaxis
Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
We consider the parabolic-elliptic model for the chemotaxis with fractional (anomalous) diffusion. Global-in-time solutions are constructed under (nearly) optimal assumptions on th…
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…
Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems
Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki +1
In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only desta…
Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data
Piotr Biler, Jacek Zienkiewicz
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than as the initial data is given. This result ha…
Precise tail asymptotics of fixed points of the smoothing transform with general weights
D. Buraczewski, E. Damek, J. Zienkiewicz
We consider solutions of the stochastic equation , where is a fixed constant, are independent, identically distributed random variables and $R…
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 +…
Local criteria for blowup in two-dimensional chemotaxis models
Piotr Biler, Tomasz Cieślak, Grzegorz Karch +1
We consider two-dimensional versions of the Keller--Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solu…
Optimal criteria for blowup of radial and -symmetric solutions of chemotaxis systems
Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
A simple proof of concentration of mass equal to for blowing up -symmetric solutions of the Keller--Segel model of chemotaxis in two dimensions with large is given. Mor…
A characterization of Hardy spaces associated with certain Schrödinger operators
Jacek Dziubański, Jacek Zienkiewicz
Let be the semigroup of linear operators generated by a Schrödinger operator on , , where satisfies $Δ^{-1} V\in L^\…
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}…