Search Results (19)

Poverty is a multifaceted phenomenon impacting millions globally, defined by a deficiency in both material and immaterial resources, which consequently restricts access to satisfactory living conditions. Comprehensive poverty analysis can be accomplished through the application of mathematical and modeling techniques, which are useful in understanding and predicting poverty trends. These models, which often incorporate principles from economics, stochastic processes, and dynamic systems, enable the assessment of the factors influencing poverty and the effectiveness of public policies in alleviating it. This paper introduces a mathematical compartmental model to investigate poverty within a population ($\psi \left(t\right)$), considering the effects of immigration, crime, and incarceration. The model aims to elucidate the interconnections between these factors and their combined impact on poverty levels. We begin the study by ensuring the mathematical validity of the model by demonstrating the uniqueness of a positive solution. Next, it is shown that under specific conditions, the probability of poverty persistence approaches certainty. Conversely, conditions leading to an exponential reduction in poverty are identified. Additionally, the semigroup associated with our model is proven to possess the Feller property, and its distribution has a unique invariant measure. To confirm and validate these theoretical results, interesting numerical simulations are performed. Full article

This paper analyzes a parabolic operator $\mathcal{L}$ that generalizes several well-known operators commonly used in financial mathematics. We establish the existence and uniqueness of the Feller semigroup associated with $\mathcal{L}$ and derive its explicit analytical representation. The theoretical framework developed in this study provides a robust foundation for modeling stochastic processes relevant to financial markets. Furthermore, we apply these findings to energy market trading by developing specialized simulation algorithms and forecasting models. These methodologies were tested across all assets comprising the S&P 500 Energy Index, evaluating their predictive accuracy and effectiveness in capturing market dynamics. The empirical analysis demonstrated the practical advantages of employing generalized semigroups in modeling non-Gaussian market behaviors and extreme price fluctuations. Full article

In this paper, we consider a class of stochastic differential equations driven by multiplicative $\alpha$-stable ($0<\alpha <2$) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a general non-explosion condition. Next, the weak Feller and stationary properties are derived. Furthermore, a concrete sufficient condition for the coefficients is presented, which is different from the conditions for SDEs driven by Brownian motion or general squared-integrable martingales. Finally, some ergodic and mixing properties are obtained by using the Foster–Lyapunov criteria. Full article

An analytical derivation of the conditional moment-generating function (MGF) for a regime-switching nonlinear drift constant elasticity of variance process is established. The proposed model incorporates both regime-switching mechanisms and nonlinear drift components to better capture market phenomena such as volatility smiles and leverage effects. Regime-switching models can match the tendency of financial markets to often change their behavior abruptly and the phenomenon that the new behavior of financial variables often persists for several periods after such a change. Closed-form formulas for the MGF under various conditions, which are then applied for option pricing, are also derived. The efficacy and accuracy of the results are validated through a discrete Markov chain simulation. The results obtained from the proposed formulas completely match with those from MC simulations, while requiring significantly less computational time. Full article

This study presents the effects of using a battery-powered chainsaw on work efficiency and ergonomics under real conditions during timber harvesting. The study was conducted during the felling and processing of coniferous and deciduous trees with a diameter at breast height (DBH) of 13 cm to 78 cm using both a petrol-powered and battery-powered chainsaw. The results include comparisons of time composition, work efficiency, psychophysical workload, and noise exposure. Heart rate and noise exposure were measured over ten days as part of a time study using the Husqvarna 543 XP petrol-powered chainsaw and the Husqvarna 540i HP battery-powered chainsaw. The comparison of the time composition between the chainsaws used showed 3%–4% differences in the duration of productive time operations and 16% in service time. The difference in work efficiency during the productive time between the two chainsaws was statistically insignificant, but generally higher when working with the battery-powered chainsaw than with the petrol-powered chainsaw. During the main productive time, the work efficiency was 9.89 min/t for the petrol-powered chainsaw and 9.44 min/t for the battery-powered chainsaw. The psychophysical workload of the feller was lower when using the battery-powered chainsaw than when using the petrol-powered chainsaw as the relative working heart rates during the entire productive time was 32.5% for the battery-powered chainsaw and 35.0% for the petrol-powered chainsaw. The noise exposure of the workers was lower when using a battery-powered chainsaw, namely 6.0 dB(A) and 0.4 dB(C) compared to the use of a petrol-powered chainsaw. The results of this paper indicate that battery-powered chainsaws can compete with petrol chainsaws in harvesting conditions that are currently considered unsuitable due to the large volume of trees. Full article

It seems that one cannot find many papers relating entropy to sport competitions. Thus, in this paper, I use (i) the Shannon intrinsic entropy (S) as an indicator of “teams sporting value” (or “competition performance”) and (ii) the Herfindahl-Hirschman index (HHi) as a “teams competitive balance” indicator, in the case of (professional) cyclist multi-stage races. The 2022 Tour de France and 2023 Tour of Oman are used for numerical illustrations and discussion. The numerical values are obtained from classical and and new ranking indices which measure the teams “final time”, on one hand, and “final place”, on the other hand, based on the “best three” riders in each stage, but also the corresponding times and places throughout the race, for these finishing riders. The analysis data demonstrate that the constraint, “only the finishing riders count”, makes much sense for obtaining a more objective measure of “team value” and team performance”, at the end of a multi-stage race. A graphical analysis allows us to distinguish various team levels, each exhibiting a Feller-Pareto distribution, thereby indicating self-organized processes. In so doing, one hopefully better relates objective scientific measures to sport team competitions. Moreover, this analysis proposes some paths to elaborate on forecasting through standard probability concepts. Full article

Lévy walks represent important modeling tools for a variety of real-life processes. Their natural scaling limits are known to be described by the so-called material fractional derivatives. So far, these scaling limits have been derived for spatially homogeneous walks, where Fourier and Laplace transforms represent natural tools of analysis. Here, we derive the corresponding limiting equations in the case of position-depending times and velocities of walks, where Fourier transforms cannot be effectively applied. In fact, we derive three different limits (specified by the way the process is stopped at an attempt to cross the boundary), leading to three different multi-dimensional versions of Caputo–Dzherbashian derivatives, which correspond to different boundary conditions for the generators of the related Feller semigroups and processes. Some other extensions and generalizations are analyzed. Full article

For the Wiener, Ornstein–Uhlenbeck, and Feller processes, we study the transition probability density functions with an absorbing boundary in the zero state. Particular attention is paid to the proportional cases and to the time-homogeneous cases, by obtaining the first-passage time densities through the zero state. A detailed study of the asymptotic average of local time in the presence of an absorbing boundary is carried out for the time-homogeneous cases. Some relationships between the transition probability density functions in the presence of an absorbing boundary in the zero state and between the first-passage time densities through zero for Wiener, Ornstein–Uhlenbeck, and Feller processes are proven. Moreover, some asymptotic results between the first-passage time densities through zero state are derived. Various numerical computations are performed to illustrate the role played by parameters. Full article

This article shows that the change of rough surfaces in the way of their contact interaction can be analyzed using the theory of Markov’s processes. In the framework of existing models, this problem cannot be solved. In this article, the idea of reducing to Markov’s model is shown on a simple discrete scheme, which is then generalized. The approach was applied to the analysis of the friction process, to the fatigue failure mode, in which the surface element changes after multiple contacts, possibly many millions. The Kolmogorov-Feller’s equations for the model of this regime were presented and the model of the influence of lubrication is offered. A calculated example of estimating the evolution of surfaces separated by a lubricant layer is given. Additionally, the technical characteristics as functions of the friction path and the load were evaluated. Full article

The identification of the second-order dependence structure of streamflow has been one of the oldest challenges in hydrological sciences, dating back to the pioneering work of H.E Hurst on the Nile River. Since then, several large-scale studies have investigated the temporal structure of streamflow spanning from the hourly to the climatic scale, covering multiple orders of magni-tude. In this study, we expanded this range to almost eight orders of magnitude by analysing small-scale streamflow time series (in the order of minutes) from ground stations and large-scale streamflow time series (in the order of hundreds of years) acquired from paleocli-matic reconstructions. We aimed to determine the fractal behaviour and the long-range de-pendence behaviour of the streamflow. Additionally, we assessed the behaviour of the first four marginal moments of each time series to test whether they follow similar behaviours as sug-gested in other studies in the literature. The results provide evidence in identifying a common stochastic structure for the streamflow process, based on the Pareto–Burr–Feller marginal dis-tribution and a generalized Hurst–Kolmogorov (HK) dependence structure. Full article

At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results; however, due to the instantaneous interest rate and instantaneous volatility in the model following the Feller square root process, only a semi-closed solution can be obtained by solving PDEs. This paper presents a simplified approach to price log-return variance swaps under the CIR–Heston hybrid model. Compared with Cao’s work, an important feature of our approach is that there is no need to solve complex PDEs; a closed-form solution is obtained by applying the martingale theory and $\mathrm{It}\widehat{\mathrm{o}}$’s lemma. The closed-form solution is significant because it can achieve accurate pricing and no longer takes time to adjust parameters by numerical method. Another significant feature of this paper is that the impact of sampling frequency on pricing formula is analyzed; then the closed-form solution can be extended to an approximate formula. The price curves of the closed-form solution and the approximate solution are presented by numerical simulation. When the sampling frequency is large enough, the two curves almost coincide, which means that our approximate formula is simple and reliable. Full article

We review and discuss the properties of various models that are used to describe the behavior of stock returns and are related in a way or another to fractional pseudo-differential operators in the space variable; we compare their main features and discuss what behaviors they are able to capture. Then, we extend the discussion by showing how the pricing of contingent claims can be integrated into the framework of a model featuring a fractional derivative in both time and space, recall some recently obtained formulas in this context, and derive new ones for some commonly traded instruments and a model involving a Riesz temporal derivative and a particular case of Riesz–Feller space derivative. Finally, we provide formulas for implied volatility and first- and second-order market sensitivities in this model, discuss hedging and profit and loss policies, and compare with other fractional (Caputo) or non-fractional models. Full article

The stochastic structures of potential evaporation and evapotranspiration (PEV and PET or ETo) are analyzed using the ERA5 hourly reanalysis data and the Penman–Monteith model applied to the well-known CIMIS network. The latter includes high-quality ground meteorological samples with long lengths and simultaneous measurements of monthly incoming shortwave radiation, temperature, relative humidity, and wind speed. It is found that both the PEV and PET processes exhibit a moderate long-range dependence structure with a Hurst parameter of 0.64 and 0.69, respectively. Additionally, it is noted that their marginal structures are found to be light-tailed when estimated through the Pareto–Burr–Feller distribution function. Both results are consistent with the global-scale hydrological-cycle path, determined by all the above variables and rainfall, in terms of the marginal and dependence structures. Finally, it is discussed how the existence of, even moderate, long-range dependence can increase the variability and uncertainty of both processes and, thus, limit their predictability. Full article

We consider the first-passage time problem for the Feller-type diffusion process, having infinitesimal drift $B_1(x,t)=\alpha \left(t\right)x+\beta \left(t\right)$ and infinitesimal variance $B_2(x,t)=2r\left(t\right)x$, defined in the space state $[0,+\infty )$, with $\alpha \left(t\right)\in \mathbb{R}$, $\beta \left(t\right)>0$, $r\left(t\right)>0$ continuous functions. For the time-homogeneous case, some relations between the first-passage time densities of the Feller process and of the Wiener and the Ornstein–Uhlenbeck processes are discussed. The asymptotic behavior of the first-passage time density through a time-dependent boundary is analyzed for an asymptotically constant boundary and for an asymptotically periodic boundary. Furthermore, when $\beta \left(t\right)=\xi r\left(t\right)$, with $\xi >0$, we discuss the asymptotic behavior of the first-passage density and we obtain some closed-form results for special time-varying boundaries. Full article

The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift $\alpha \left(t\right)x+\beta \left(t\right)$ and infinitesimal variance $2r\left(t\right)x$, with a zero-flux condition in the zero-state, is considered. This process is obtained as a continuous approximation of a birth-death process with immigration. The transition probability density function and the related conditional moments, with their asymptotic behaviors, are determined. Special attention is paid to the cases in which the intensity functions $\alpha \left(t\right)$, $\beta \left(t\right)$, $r\left(t\right)$ exhibit some kind of periodicity due to seasonal immigration, regular environmental cycles or random fluctuations. Various numerical computations are performed to illustrate the role played by the periodic functions. Full article