Abstract
We present a new characterization of real homogeneous functions of a negative degree by a new counterpart of Euler’s homogeneous function theorem using quantum calculus and replacing the classical derivative operator by a -derivative operator. As an application we study the solution of the Cauchy problem associated to the -analogue of the Euler operator. Using this solution, a probabilistic interpretation is given in some details; more specifically, we prove that this solution is a stochastically continuous markovian transition operator. Finally, we study it’s associated subordinated stochastically markovian transition operator.
Citation
Moncef Elghribi. "A NEW CHARACTERIZATION OF HOMOGENEOUS FUNCTIONS AND APPLICATIONS." Rocky Mountain J. Math. 53 (4) 1073 - 1085, August 2023. https://doi.org/10.1216/rmj.2023.53.1073
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