This paper explores the capabilities of machine learning for probabilistic forecasting fractional Brownian motion (fBm). The focus is on predicting probability value an fBm time series exceeding a certain threshold after specific number steps, given only knowledge its Hurst exponent. study aims to determine if self-similarity property preserved in and which algorithms are most effective. Two ty...

Planning and development decisions in both the government business sectors often require small area population forecasts. Unfortunately, current methods produce forecasts that are inaccurate, particularly for remote areas those with smaller populations. Such inaccuracy necessitates evaluation of to forecast communicate uncertainty, however, little research has been conducted this domain In pape...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

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.

In this paper, we define the concepts of modified intuitionistic probabilistic metric spaces, the property (E.A.) and  the common property (E.A.) in   modified  intuitionistic probabilistic metric spaces.Then, by the commonproperty (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.

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.