2 citations · 3 across the 5 of their papers we have counts for
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Regularization inequalites for one-dimensional Cauchy-type measures
Tomasz Byczkowski, Tomasz Żak
In the paper we investigate various inequalities for the one-dimensional Cauchy measure. We also consider analogous properties for one-dimensional sections of multidimensional isot…
Space and time inversions of stochastic processes and Kelvin transform
Larbi Alili, Loïc Chaumont, Piotr Graczyk +1
Let be a standard Markov process. We prove that a space inversion property of implies the existence of a Kelvin transform of -harmonic, excessive and operator-harmonic f…
Inversion, duality and Doob -transforms for self-similar Markov processes
Larbi Alili, Loïc Chaumont, Piotr Graczyk +1
We show that any -valued self-similar Markov process , with index can be represented as a path transformation of some Markov additive process (…
Supremum distribution of Bessel process of drifting Brownian motion
Andrzej Pyć, Grzegorz Serafin, Tomasz Żak
Let (B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t + μt) be a three-dimensional Brownian motion with drift μ, starting at the origin. Then X_t = ||(B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t +μt)||, its di…
On inversions and Doob -transforms of linear diffusions
L. Alili, P. Graczyk, T. Zak
Let be a regular linear diffusion whose state space is an open interval . We consider a diffusion which probability law is obtained as a Doob -tr…