The subject of this paper is a fragmentation equation with non-conservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the fragmentation rate, we describe the largetime behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equation ar...

In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

<p style='text-indent:20px;'>We develop a backward stochastic differential equation based probabilistic machine learning method, which formulates class of neural networks as optimal control problem. An efficient gradient descent algorithm is introduced with the computed through equation. Convergence analysis for optimization and numerical experiments applications are carried out to valida...

We give a tutorial exposition of the analogue filtering equation for quantum systems focusing on probabilistic framework and developing ideas from classical theory. Quantum covariances conditional expectations von Neumann algebras play an essential part in presentation.

In this paper, a general formula of disparity estimation based on Bayesian Maximum A Posteriori (MAP) algorithm is derived and implemented with simplified probabilistic models. The formula is the generalized probabilistic diffusion equation based on Bayesian model, and can be implemented into some different forms corresponding to the probabilistic models in the disparity neighborhood system or ...

We discuss the differential equation method for establishing dynamic concentration of discrete random processes. present several relatively simple examples it and aim to make understandable unfamiliar reader who has some basic knowledge on probabilistic methods, graphs equations.

Here we present an approach to problems of diffraction that has its roots in a number of well-established theories such as the geometric theory of diffraction, the method of parabolic equations, the theory of Wiener functional integration, and the theory of stochastic processes. We start our analysis of the Helmholtz equation following closely the scheme of the ray method, but instead of approx...

the current study investigated and compared data generation methods for groundwater modeling. thesemethods can be divided into two classes; geostatistic and probabilistic. by comparing geostatistic methods,the best method was chosen and the hydraulic conductivity of the aquifer was generated for a study area ina grid (9-cell) format. after observing weak spatial correlation between the data, th...

We analyze a class of nonlinear partial differential equations (PDEs) defined on <mml:mi mathva...