Related papers: On the differentiability of interval functions
The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are…
We study the large deviations of Markov chains under the sole assumption that the state space is discrete. In particular, we do not require any of the usual irreducibility and exponential tightness assumptions. Using subadditive arguments,…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
Estimates of some integrals related to variations of smooth functions are presented.
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…
Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. The estimates are uniform with respect to all graphs of a given finite length, and the constant factors in the…
In this paper, we consider a subclass of starlike functions associated with a vertical strip domain. Several results concerned with integral representations, convolutions, and coefficient inequalities for functions belonging to this class…
In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment…
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in…
In this paper, using the tools from the lineability theory, we distinguish certain subsets of $p$-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…
This paper presents a collection of useful formulas of dynamic derivatives on time scales, systematically collected for reference purposes. As an application, we define trigonometric and hyperbolic functions on time scales in such a way the…
In this paper, some sufficient conditions for the differentiability of the $n$-variable real-valued function are obtained, which are given based on the differentiability of the $n-1$-variable real-valued function and are weaker than…
We investigate the cutoff phenomenon for Markov processes under information divergences such as $f$-divergences and R\'enyi divergences. We classify most common divergences into four types, namely $L^2$-type, $\mathrm{TV}$-type,…
Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…
Semi-Markov processes are a generalization of Markov processes since the exponential distribution of time intervals is replaced with an arbitrary distribution. This paper provides an integro-differential form of the Kolmogorov's backward…