Zobrazeno 1 - 10
of 74
pro vyhledávání: '"MALECKI, JACEK"'
Autor:
Burdzy, Krzysztof, Małecki, Jacek
We prove Archimedes' principle for a macroscopic ball in ideal gas consisting of point particles with non-zero mass. The main result is an asymptotic theorem, as the number of point particles goes to infinity and their total mass remains constant. We
Externí odkaz:
http://arxiv.org/abs/2102.01718
Autor:
Chaumont, Loïc, Małecki, Jacek
Let $p_t(x)$, $f_t(x)$ and $q_t^*(x)$ be the densities at time $t$ of a real L\'evy process, its running supremum and the entrance law of the reflected excursions at the infimum. We provide relationships between the asymptotic behaviour of $p_t(x)$,
Externí odkaz:
http://arxiv.org/abs/1912.04193
Autor:
Chaumont, Loïc, Małecki, Jacek
We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric L\'evy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we express the dens
Externí odkaz:
http://arxiv.org/abs/1901.09106
Autor:
Małecki, Jacek, Stempak, Krzysztof
Publikováno v:
Studia Mathematica 251 (2020), 171-193
For an open subset $\Omega$ of $\mathbb R^d$, symmetric with respect to a hyperplane and with positive part $\Omega_+$, we consider the Neumann/Dirichlet Laplacians $-\Delta_{N/D,\Omega}$ and $-\Delta_{N/D,\Omega_+}$. Given a Borel function $\Phi$ on
Externí odkaz:
http://arxiv.org/abs/1901.02851
Autor:
Małecki, Jacek, Pérez, José Luis
We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that the famil
Externí odkaz:
http://arxiv.org/abs/1901.02841
Akademický článek
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Autor:
Chaumont, Loïc, Małecki, Jacek
We provide short and simple proofs of the continuous time ballot theorem for processes with cyclically interchangeable increments and Kendall's identity for spectrally positive L\'evy processes. We obtain the later result as a direct consequence of t
Externí odkaz:
http://arxiv.org/abs/1804.06371
Autor:
Graczyk, Piotr, Malecki, Jacek
We study the existence and uniqueness of SDEs describing squared Bessel particles systems in full generality. We define non-negative and non-colliding squared Bessel particle systems and we study their properties.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1707.06295
Autor:
Malecki, Jacek, Serafin, Grzegorz
We provide sharp two-sided estimates on the Dirichlet heat kernel $k_1(t,x,y)$ for the Laplacian in a ball. The result accurately describes the exponential behaviour of the kernel for small times and significantly improves the qualitatively sharp res
Externí odkaz:
http://arxiv.org/abs/1612.01833
Publikováno v:
Stochastic Processes and their Applications,Vol 128, Issue 4, April 2018, pp. 1386-1404
A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in terms of
Externí odkaz:
http://arxiv.org/abs/1607.00206