http://popups.lib.uliege.be/1373-5411/index.php?id=3007 Publications of Auteurs Vadim F. Krotov fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=3001 Parametrical families of distributions are considered, characterised by Borel's measure, infinitisimal in parameters space. The latter property defines the construction of the family and each its member. The properties of this construction are studied, as well as techniques of synthesis of probabilistic distributions, and application areas, first of all quantum systems. They are defined as infinitisimal dynamic systems, observation results of which are described by above mentioned families with the wave function as a parameter. We have demonstrated that axiomatic system of the quantum mechanics is overdefined ("redundant" axioms are restated as theorems), as well as showed new statistical properties of relativistic quantum mechanics. We also proposed non- contradictive model to explain some paradoxal properties of quantum field (paradox of the boson field energy). Wed, 04 Sep 2024 11:34:22 +0200 Wed, 04 Sep 2024 11:34:37 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3001 http://popups.lib.uliege.be/1373-5411/index.php?id=860 The stochastic dynamical system with the states described by elements u of a Hilbert space is considered. There is a deterministic system considered as its nonperturbed variant. An outcome y is observed under random perturbations. The probability distribution P(y, u) of the measurements results in the fixed states u is analysed. A class of stochastic systems marked by the full determination of the law P(y, u) via equations of the nonperturbed system is found. We also find the distributions P(y, u). These distributions prove to be similar to the quantum laws of probability distribution of observable quantities including the principles of superposition and uncertainty and the phenomenon of quantization. Mon, 01 Jul 2024 14:03:02 +0200 Thu, 10 Oct 2024 10:42:58 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=860