Mateusz Kwaśnicki

activity

20102019

collaborators

6 papers

math.PR2019

Boundary traces of shift-invariant diffusions in half-plane

Mateusz Kwaśnicki

We study boundary traces of shift-invariant diffusions: two-dimensional diffusions in the upper half-plane $R \times [0, \infty)$ (or in $R \times [0, R)$ ) invari…

math.PR2019

Characterisation of the class of bell-shaped functions

Mateusz Kwaśnicki, Thomas Simon

A non-negative function $f$ is said to be 'bell-shaped' if $f$ tends to zero at $\pm \infty$ and the $n$ -th derivative of $f$ changes its sign $n$ times for every $n = 0, 1, 2, \ld…

math.AP2019

Harmonic extension technique for non-symmetric operators with completely monotone kernels

Mateusz Kwaśnicki

We identify a class of non-local integro-differential operators $K$ in $R$ with Dirichlet-to-Neumann maps in the half-plane $R \times (0, \infty)$ for appropriate…

math.PR2019

Random walks are determined by their trace on the positive half-line

Mateusz Kwaśnicki

We prove that the law of a random walk $X_{n}$ is determined by the one-dimensional distributions of $max (X_{n}, 0)$ for $n = 1, 2, \dots$ , as conjectured recently by Loïc Chaumont a…

math.PR2018

Fluctuation theory for Lévy processes with completely monotone jumps

Mateusz Kwaśnicki

We study the Wiener-Hopf factorization for Lévy processes $X_{t}$ with completely monotone jumps. Extending previous results of L.C.G. Rogers, we prove that the space-time Wiener-Hop…

math.SP2010

Eigenvalues of the fractional Laplace operator in the interval

Mateusz Kwaśnicki

Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional fractional Laplace operator (-d^2/dx^2)^(alpha/2) (0 < alpha < 2) in the interval (-1,1) is given: the n-th…