Technique Of Subordination Research Articles

Geometric Properties Connected with a Certain Multiplier Integral q−Analogue Operator

The topic concerning the introduction and investigation of new classes of analytic functions using subordination techniques for obtaining certain geometric properties alongside coefficient estimates and inclusion relations is enriched by the results of the present investigation. The prolific tools of quantum calculus applied in geometric function theory are employed for the investigation of a new class of analytic functions introduced by applying a previously defined generalized q−integral operator and the concept of subordination. Investigations are conducted on the new class, including coefficient estimates, integral representation for the functions of the class, linear combinations, forms of the weighted and arithmetic means involving functions from the class, and the estimation of the integral means results.

Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift.

The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the trapping phase) in a disordered medium is considered in the presence of an external drift. In particular, we consider trapping events whose times follow a scale-free distribution with diverging mean trapping time. We construct this process in terms of fractional Brownian motion with constant forcing in which the trapping effect is introduced by the subordination technique, connecting "operational time" with observable "real time." We derive the statistical properties of this process such as non-Gaussianity and nonergodicity, for both ensemble and single-trajectory (time) averages. We demonstrate nice agreement with extensive simulations for the probability density function, skewness, kurtosis, as well as ensemble and time-averaged mean-squared displacements. We place a specific emphasis on the comparisons between the cases with and without drift.

Certain sufficient conditions for phi-like functions in a parabolic region

To obtain the main result of the present paper we use the technique of differential subordination. As special cases of our main result, we obtain sufficient conditions for $f\in\mathcal A$ to be $\phi-$like, starlike and close-to-convex in a parabolic region.

Subdiffusion in the Presence of Reactive Boundaries: A Generalized Feynman–Kac Approach

We derive, through subordination techniques, a generalized Feynman–Kac equation in the form of a time fractional Schrödinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through a stochastic treatment how this generalized Feynman–Kac equation describes subdiffusive processes with reactions. In this interpretation, the subordinated local time represents the number of times a specific spatial point is reached, with the amount of time spent there being immaterial. This distinction provides a practical advance due to the potential long waiting time nature of subdiffusive processes. The subordinated local time is used to formulate a probabilistic understanding of subdiffusion with reactions, leading to the well known radiation boundary condition. We demonstrate the equivalence between the generalized Feynman–Kac equation with a reflecting boundary and the fractional diffusion equation with a radiation boundary. We solve the former and find the first-reaction probability density in analytic form in the time domain, in terms of the Wright function. We are also able to find the survival probability and subordinated local time density analytically. These results are validated by stochastic simulations that use the subordinated local time description of subdiffusion in the presence of reactions.

Some Subordination Results Defined by Using the Symmetric q-Differential Operator for Multivalent Functions

In this article, we use the concept of symmetric q-calculus and convolution in order to define a symmetric q-differential operator for multivalent functions. This operator is an extension of the classical Ruscheweyh differential operator. By using the technique of differential subordination, we derive several interesting applications of the newly defined operator for multivalent functions.

Final state observability in Banach spaces with applications to subordination and semigroups induced by Lévy processes

This paper generalizes the abstract method of proving an observability estimate by combining an uncertainty principle and a dissipation estimate. In these estimates we allow for a large class of growth/decay rates satisfying an integrability condition. In contrast to previous results, we use an iterative argument which enables us to give an asymptotically sharp estimate for the observation constant and which is explicit in the model parameters. We give two types of applications where the extension of the growth/decay rates naturally appear. By exploiting subordination techniques we show how the dissipation estimate of a semigroup transfers to subordinated semigroups. Furthermore, we apply our results to semigroups related to Lévy processes.

COMPLEX MATHEMATICAL MODELING FOR ADVANCED FRACTAL–FRACTIONAL DIFFERENTIAL OPERATORS WITHIN SYMMETRY

Non-local operators of differentiation are bestowed with capabilities of encompassing complex natural into mathematical equations. Symmetry as invariance under a specified group of transformations can allow for the concept to be applied extensively not only to spatial figures but also to abstract objects like mathematical expressions which can be said to be expressions of physical relevance, in particular dynamical equations. Derived from this point of view, it can be noted that the more complex physical problems are, the more complex mathematical operators of differentiation are required. Accordingly, the fractal–fractional operators (FFOs) are expanded into the complex plane in our research which revolves around a unique class of normalized analytic functions in the open unit disk. To bring FFOs (differential and integral) into the normalized class, the study aims to expand and modify them along with the investigation of the FFOs geometrically. The qualities of convexity and starlikeness are implicated in this study where the differential subordination technique serves as the foundation for the inquiry under consideration. Furthermore, a collection of differential FFO inequalities is taken into account, demonstrating that the normalized Fox–Wright function can contain all FFOs. Besides these steps, the concept of Grunsky factors is applied to investigate symmetry, while boundary value issues involving FFOs are probed. Consequently, the related properties and applications can be further developed, which requires the devotion to differential fractional problems and diverse complex problems in relation to viable applications, pointing out the room to modify and upgrade the existing methods for more optimal outcomes in challenging real-world problems.

Briot–Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function

We define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investigate several new results related to the Briot–Bouquet differential subordinations for the linear operator involving the normalized form of the generalized Struve function. We also obtain univalent solutions to the Briot–Bouquet differential equations and observe that these solutions are the best dominant of the Briot–Bouquet differential subordinations for the exponential starlike function class. Moreover, we give an application of fractional integral operator for a complex-valued function associated with the generalized Struve function. The significance of this paper is due to the technique employed in proving the results and novelty of these results for the Struve functions. The approach used in this paper can lead to several new problems in geometric function theory associated with special functions.

On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc

The Bessel–Struve kernel function defined in the unit disc is used in this study. The Bessel–Struve kernel functions are generalized in this article, and differential equations are derived. We found conditions under which the generalized Bessel–Struve function is Lemniscate convex by using a subordination technique. The relation between the Janowski class and exponential class is also derived.

Bochner's subordination and fractional caloric smoothing in Besov and Triebel–Lizorkin spaces

AbstractWe use Bochner's subordination technique to obtain caloric smoothing estimates in Besov‐ and Triebel–Lizorkin spaces. Our new estimates extend known smoothing results for the Gauß–Weierstraß, Cauchy–Poisson and higher‐order generalized Gauß–Weierstraß semigroups. Extensions to other function spaces (homogeneous, hybrid) and more general semigroups are sketched.

Sandwich type results for meromorphic functions with respect to symmetrical points

In the present paper, we use the technique of differential subordination and superordination involving meromorphic functions with respect to symmetric points and also derive some sandwich results. As a consequence of main result, we obtain results for meromorphic starlike functions with respect to symmetrical points.

Realized Quantiles*

This article proposes a simple approach to estimate quantiles of daily financial returns directly from high-frequency data. We denote the resulting estimator as realized quantile (RQ) and use it to forecast tail risk measures, such as Value at Risk (VaR) and Expected Shortfall (ES). The RQ estimator is built on the assumption that financial logarithm prices are subordinated self-similar processes in intrinsic time. The intrinsic time dimension stochastically transforms the clock time in order to capture the real “heartbeat” of financial markets in accordance with their trading activity and/or riskiness. The self-similarity assumption allows to compute daily quantiles by simply scaling up their intraday counterparts, while the subordination technique can easily accommodate numerous empirical features of financial returns, such as volatility persistence and fat-tailedness. Our method, which is built on a flexible assumption, is simple to implement and exploits the rich information content of high-frequency data from another time perspective than the classical clock time. In a comprehensive empirical exercise, we show that our forecasts of VaR and ES are more accurate than the ones from a large set of up-to-date comparative models, for both, stocks and foreign exchange rates.

Non-Gaussian diffusion of mixed origins

The properties of diffusion processes are drastically affected by heterogeneities of the medium that can induce non-Gaussian behavior of the propagator in contrast with the idealized realm of Brownian motion. In this paper we analyze the diffusion propagator when distinct origins of heterogeneity (e.g. time-fractional diffusion, diffusing diffusivity, distributed diffusivity across a population) are combined. These combinations allow one to describe new classes of strongly heterogeneous processes relevant to biology. Based on a combined subordination technique, we obtain the exact propagator for different instructive examples. This approach is then used to calculate analytically the first-passage time statistics (on half-real line and in any bounded domain) for a particle undergoing non-Gaussian diffusion of mixed origins.

Financial modelling applying multivariate Lévy processes: New insights into estimation and simulation

In general, daily or intra-day stock returns are fat-tailed and heavily skewed. Lévy processes fulfil these modelling requirements and produce marginal distributions with finite variances. An extensive body of literature looks into the fittings and applications of single processes. In contrast, our analysis of multivariate Lévy models finds applications in pricing multivariate options or in portfolio and risk management. We use the technique of multivariate subordination and conduct a large simulation study on the fitting of the αρGH, αρNIG, and αρVG models in order to identify the best fitting method for multivariate Lévy processes, as well as the best multivariate model overall. Our findings confirm previous results in the literature, namely that the MLE is the best estimation approach in a two-step fitting procedure and the αρGH model is the best multivariate model. It reveals that also the χ2 method is appropriate.

Reconsidering Palmer v Thompson

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Application of Srivastava-Attiya Operator to the Generalization of Mocanu Functions

In this paper we introduce certain subclasses of analytic functions by applying Srivastava-Attiya operator. Our main purpose is to derive inclusion results by using concept of conic domain and subordination techniques. We also deduce some new as well as well-known results from our investigations.

Argentina's Curse, Venezuela's Blessing: How to Restructure Venezuela's Debt Using Pari Passu

Given the depth of Venezuela’s economic crisis, many fear that the government and the state-owned oil company Petroleos de Venezuela, S.A. (“PDVSA”) are on the brink of insolvency. In this paper, we introduce a restructuring plan that would allow Venezuela to restructure its external debt in an orderly manner. We propose that Venezuela restructure both PDVSA debt and its own external debt via Exchange Offers. To maximize the number of participating bondholders and receive sufficient debt relief, we suggest that Venezuela primarily utilize the pari passu clauses in the vast majority of PDVSA and Venezuelan bonds, which have been modified compared to a typical pari passu clause and can be read to allow the subordination of the bonds according to Venezuelan law. To minimize the number of holdout creditors, therefore, Venezuela can introduce a law that subordinates non-exchanged debt to exchanged debt, making timely or full payment of holdout debt unlikely. This tactic would minimize the need to solely rely on alternative restructuring techniques, such as exit consents and Collective Action Clauses. We argue that while these techniques might in and of themselves prove insufficient to effectuate a successful restructuring, they could be useful when viewed as second-best restructuring options. Because the parties contracted for debt subordination in the bond contracts, we predict that using a debt subordination technique would be more viable in Venezuela’s case than it has been in past sovereign debt restructurings. Ironically, the pari passu clause that doomed Argentina might be what saves Venezuela.

Modeling Dependent Outages of Electric Power Plants

In the article “Modeling Dependent Outages of Electric Power Plants,” Malladi, Mendoza-Arriaga, and Tompaidis study simultaneous outages of many electric power plants, a problem that can have severe economic consequences. Using real data, they separate power plants into possibly overlapping groups. Each group is affected by a single cause—input fuel, geographic proximity, or location relative to the transmission network, for example. Using the mathematical technique of time subordination, the authors build dependence in outages among power plants in each group. With outage data from NERC, they determine these groups for Texas and the western United States and calculate the impact on system reliability and on the addition of new generation assets. Looking ahead, the methodology in the article can help account for dependence in generation from renewable sources as their share of generation capacity increases. The article will be of interest to owners of generating assets, regulators, and energy and reliability researchers.

Feynman–Kac equation for anomalous processes with space- and time-dependent forces

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman–Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman–Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman–Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman–Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Q-Harmonic mappings for which analytic part is $q-$ convex functions of complex order

We introduce a new class of harmonic function $f$, that is subclass of planar harmonic mapping associated with $q-$difference operator. Let $h$ and $g$ are analytic functions in the open unit disc $\mathbb{D}=\{ z\,:\,|z|<1 \}$. If $f=h+\bar{g}$ is the solution of the non-linear partial differential equation $w_q(z)=\dfrac{D_q g(z)}{D_q h(z)}=\dfrac{\bar{f}_\bar{z}}{f_z}$ with $|w_q(z)|<1$, $w_q(z)\prec b_1 \dfrac{1+z}{1-qz}$ and $h$ is $q-$convex function of complex order, then the class of such functions are called $q-$harmonic functions for which analytic part is $q-$convex functions of complex order denoted by $\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)}$. Obviously that the class $\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)}$ is the subclass of $\mathcal{S}_\mathcal{H}$. In this paper, we investigate properties of the class $\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)}$ by using subordination techniques.