We consider the renewal counting number process N = N(t) as a forward march over the non-negative integers with independent identically distributed waiting times. We embed the values of the counting numbers N in a “pseudo-spatial” non-negative half-l...
Each charging/discharging cycle leads to a gradual decrease in the battery’s capacity. The degradation of capacity in lithium-ion batteries represents a non-monotonous process with random jumps. Earlier studies claimed that the instantaneous de...
For lithium-ion batteries and supercapacitors in hybrid power storage facilities, both steady degradation and random shock contribute to their failure. To this end, in this paper, we propose to introduce the degradation-threshold-shock (DTS) model fo...
This paper proposes a new fractional Poisson process through a recursive fractional differential governing equation. Unlike the homogeneous Poison process, the Caputo derivative on the probability distribution of k jumps with respect to time is linke...
This paper investigates a new class of fractional stochastic differential systems with non-Gaussian processes and Poisson jumps. Firstly, we examine the solvability results for the considered system. Furthermore, new stability results for the propose...
The article considers the fractional Poisson process as a mathematical model of deformation activity in a seismically active region. The dislocation approach is used to describe five modes of the deformation process. The change in modes is determined...
This paper consists of a general consideration of a seismic system as a subsystem of another, larger system, exchanging with it by extensive dynamical quantities in a sequential push mode. It is shown that, unlike an isolated closed system described...
We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with b...
In this paper, we introduce and study fractional versions of the Bell–Touchard process, the Poisson-logarithmic process and the generalized Pólya–Aeppli process. The state probabilities of these compound fractional Poisson processe...
To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality. Seismicity...
This paper investigates the complex behaviors and entropy properties for a novel random complex interacting stock price dynamics, which is established by the combination of stochastic contact process and compound Poisson process, concerning with stoc...
In traditional finance, option prices are typically calculated using crisp sets of variables. However, as reported in the literature novel, these parameters possess a degree of fuzziness or uncertainty. This allows participants to estimate option pri...
In this survey we stress the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus. We first start with the analytical properties of the classical Mittag-Leffler function as derived from being the...
The paper deals with a fractional time-changed stochastic risk model, including stochastic premiums, dividends and also a stochastic initial surplus as a capital derived from a previous investment. The inverse of a
Anomalous deviations from the Beer-Lambert law have been observed for a long time in a wide range of application. Despite all the attempts, a reliable and accepted model has not been provided so far. In addition, in some cases the attenuation of radi...
This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory,...
This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these results are...
Because of the nonlocal and nonsingular properties of fractional derivatives, they are more suitable for modelling complex processes than integer derivatives. In this paper, we use a fractional factor to investigate the fractional Hamilton’s ca...
The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law...
In this work, we introduce a generalization of the differential polynomial neural network utilizing fractional calculus. Fractional calculus is taken in the sense of the Caputo differential operator. It approximates a multi-parametric function with p...
In this article, we introduce the Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular, we discuss the space-fractional Skellam process and tempered space-fractional Skellam pr...
This paper addresses the generalization of counting processes through the age formalism of Lévy Walks. Simple counting processes are introduced and their properties are analyzed: Poisson processes or fractional Poisson processes can be recovered as p...
Elastic moduli are important mechanical properties that describe a material’s stiffness and its deformation under elastic loading. In addition to experimental techniques, computational homogenization is commonly used for composite materials to...
Multi-modal image fusion can provide more image information, which improves the image quality for subsequent image processing tasks. Because the images acquired using photon counting devices always suffer from Poisson noise, this paper proposes a new...
A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy manageme...
We consider a stochastic differential equation (SDE) governed by a fractional Brownian motion
Lifetime reproductive output (LRO), also called lifetime reproductive success (LRS) is often described by its mean (total fertility rate or net reproductive rate), but it is in fact highly variable among individuals and often positively skewed. Sever...
Compared with the single-component metal plate, there is a special transition layer on the joint interface between two kinds of materials in the stainless steel-carbon steel laminated plate (SCLP). In order to describe the finite element model of las...
The deformation mechanisms of classic lattice topologies (e.g., Cubic, Diamond, Octet, and Double Pyramid lattices) and their specific density-dependent mechanical properties have already been thoroughly explored by the scientific community. This stu...
Expected utility theory is critical for modeling rational decision making under uncertainty, guiding economic agents as they seek to optimize outcomes. Traditional methods often require restrictive assumptions about underlying stochastic processes, l...
This letter analyzes the meta-distribution of the transmission success probability (TSP) for vehicular networks based on a one-dimensional Poisson point process (PPP). We also propose a method to maximize the throughput across the vehicular network....
In this paper, a 2D mesoscale finite element (FE) numerical model of mortar, considering the influence of the ITZ, was proposed to evaluate the corrosion of mortar in sodium sulfate. On the mesoscale, the corroded mortar was regarded as a three-phase...
Powder densification through uniaxial compaction is governed by a number of simultaneous processes taking place on a reduced time as the result of the stress gradients within the packing, as well as the frictional and adhesive forces between the powd...
Natural terrains created by long-term erosion processes can sometimes have spectacular forms and shapes. The visible form depends often upon internal geological structure and materials. One of the unique terrain artefacts occur in the form of table m...
This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by...
In this paper, the issue of self-compacting concrete (SCC) with the addition of polyethylene terephthalate (PET) recycled aggregate is addressed. The PET utilized was a waste fraction in the PET-bottle-recycling process. The implementation of waste i...
This article analyses a four-dimensional stochastic queueing-inventory system with multiple server vacations and a state-dependent arrival process. The server can start multiple vacations at a random time only when there is no customer in the waiting...
Data networks are naturally prone to interferences that can corrupt messages, leading to performance degradation or even to critical failure of the corresponding distributed system. To improve resilience of critical systems, time-triggered networks a...
A variety of current experiments and molecular dynamics computations are expanding our understanding of rate processes occurring in extreme environments, especially at low temperatures, where deviations from linearity of Arrhenius plots are revealed....
Characterizing the top seal integrity of organic-rich caprock shale is critical in hydrocarbon exploration and fluid storage sites assessment because the caprock acts as a barrier to the low-density upward migrating fluids. This study investigated th...
The transition zone (TZ) of hydrocarbon reservoirs is an integral part of the hydrocarbon pool which contains a substantial fraction of the deposit, particularly in carbonate petroleum systems. Consequently, knowledge of its thickness and petrophysic...