85 citations · 253 across the 31 of their papers we have counts for
12 papers · 1 filter
On squared Bessel particle systems
Piotr Graczyk, Jacek Malecki
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 syste…
A Characterization of Wishart Processes and Wishart Distributions
Piotr Graczyk, Jacek Malecki, Eberhard Mayerhofer
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 diffe…
Wallach sets and squared Bessel particle systems
Piotr Graczyk, Jacek Malecki
We determine the classical and the non-central Wallach sets and by classical probabilistic methods. We prove the Mayerhofer conjecture on . We exploit the fact that $(…
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 (…
Strong solutions of non-colliding particle systems
Piotr Graczyk, Jacek Malecki
We study systems of stochastic differential equations describing positions x_1,x_2,...,x_p of p ordered particles, with inter-particles repulsions of the form H_{ij}(x_i,x_j)/(x_i-…
Fisher Information and Exponential Families Parametrized by a Segment of Means
Piotr Graczyk, Salha Mamane
We consider natural and general exponential families on parametrized by the means. We study the submodels parametr…