Related papers: On the differentiability of interval functions
The paper considers a stochastic differential equation of Duffing type with Markov coefficients. The existence of unpredictable solutions is considered. The unpredictability is a property of bounded functions characterized by unbounded…
This paper addresses the problem of evaluating a subset of the range of a vector-valued function. It is based on a work by Gold- sztejn and Jaulin which provides methods based on interval analysis to address this problem when the dimension…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…
In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…
In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The…
We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are…
Some notes and observations on analytic functions defined on an annulus
We introduce a Markov-functional approach to construct local volatility models that are calibrated to a discrete set of marginal distributions. The method is inspired by and extends the volatility interpolation of Bass (1983) and Conze and…
The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems…
In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a…
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
In the study of one dimensional dynamical systems one often assumes that the functions involved have a negative Schwarzian derivative. In this paper we consider a generalization of this condition. Specifically, we consider the interval…
The paper gives a brief account of the spaces of interval functions defined through the concepts of H-continuity, D-continuity and S-continuity. All three continuity concepts generalize the usual concept of continuity for real (point…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…
In this paper we introduce the concept of \emph{multivector functionals.} We study some possible kinds of derivative operators that can act in interesting ways on these objects such as, e.g., the $A$-directional derivative and the…
Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with $L_2$ semigroups under minimal conditions on the state space and the process trajectories; for example, no strong…
We review and develop two little known results on the equality of mixed partial derivatives which can be considered the best results so far available in their respective domains. The former, due to Mikusi\'nski and his school, deals with…