Related papers: Derivative Preserving Conditions in Conditional Ex…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
In this paper, we consider the problem of order preservation under addition and multiplication operators over the vector space of univariate real-valued random variables. Consistent with the case of usual order over the real numbers-as…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
Derivatives of fractional order are introduced in different ways: as left-inverse of the fractional integral or by generalizing the limit of the difference quotient defining integer-order derivatives. Although the two approaches lead (under…
We give a characterization of conditional expectation operators through a disjointness type property similar to band preserving operators. We say that the operator $T:X\to X$ on a Banach lattice $X$ is semi band preserving if and only if…
In the present paper, we consider nonlinear Markov operators, namely polynomial stochastic operators. We introduce a notion of orthogonal preserving polynomial stochastic operators. The purpose of this study is to show that surjectivity of…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
This paper deals with the enumeration of the higher order non-trivial compositions of the differential operations and the directional derivative in the space $R^n$ ($n \geq 3$). We present the recurrences for a counting the higher order…
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the…
Conditional displacement with a qubit ancilla is a critical component in continuous-variable error correction protocols. We present the generalized conditional displacement operator, conditioned on a qudit ancilla, and explore potential…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
We propose new numerical approach to non-conservative dynamical systems. Our method being of low order, enhances qualitative performance of standard discrete gradient algorithm, thank to new concept of a reservoir. Paper is of explanatory…
At the COSAEF conference in 2021, several participants asked the question whether a conditional expectation operator in the sense of Kuo, Labaushagne and Watson could be constructed in vector lattices other than $\mathcal{L}_p$ spaces and…
In this study, depending on the upper and the lower indices of the hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are obtained. It is shown that generalized harmonic number and hyperharmonic number can be obtained from…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…
In this paper two theorems which describe dissipative boundary conditions for ordinary differential operators on a closed interval are proved. We also show that all these boundary conditions are Birkhoff regular in even case. In odd case…
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
We introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on ${a,b}$. We show that the variance of the passage time can be expressed in terms of these derivatives. We…