Related papers: Derivative Preserving Conditions in Conditional Ex…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
In this paper we introduce a sublinear conditional operator with respect to a family of possibly nondominated probability measures in presence of multiple ordered default times. In this way we generalize the results of [5], where a…
We consider structure-preserving methods for conservative systems, which rigorously replicate the conservation property yielding better numerical solutions. There, corresponding to the skew-symmetry of the differential operator, that of…
Higher order moment estimates for solutions to nonlinear SPDEs governed by locally-monotone operators are obtained under appropriate coercivity condition. These are then used to extend known existence and uniqueness results for nonlinear…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…
Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…
In this paper we extend the definition of time conditional G-expectations $\mathbb{\hat{E}}_{t}[\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time…
In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter (first-order) derivative, the parameter can be estimated online. To analyze the…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…
A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small…
There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…
This study developed a novel formulation of conditional expectations within the framework of a jump-diffusion mean-field stochastic differential equation. We introduce an integrated approach that combines unconditioned expectations with…
In this paper we consider a generalized conditional-type Holder- inequality and investigate some classic properties of multiplication conditional expectation type operators on Orlicz-spaces.
This article deals with higher order Caputo fractional variational problems with the presence of delay in the state variables and their integer higher order derivatives.
Consider a pair of random vectors $(\mathbf{X},\mathbf{Y}) $ and the conditional expectation operator $\mathbb{E}[\mathbf{X}|\mathbf{Y}=\mathbf{y}]$. This work studies analytic properties of the conditional expectation by characterizing…
The basic purpose of the present paper is the full solutions of the inverse problem (i.e. a finding of necessary and sufficient conditions) for the operator with complex periodic coefficients.
Given a normalized state-vector $\psi $, we define the conditional expectation $\mathbb{E }_{\psi } (A | B ) $ of a Hermitian operator $A $ with respect to a strongly commuting family of self-adjoint operators $B $ as the best…