Search Results (820)

This paper deals with a system of G-stochastic differential equations with jumps, driven by G-Brownian motion and the G-Lévy process. By using Burkholder–Davis–Gundy inequalities, we prove the moment estimate and the Hölder regularity of the solution, under the linear growth and the global Lipschitz conditions of the coefficients with respect to the state variable uniformly in the time variable. Moreover, different stability properties are proved. Some illustrative examples from finance are employed in order to support our theoretical results. Full article

This work is devoted to the analysis of the limit behavior of the solution to a class of fractional stochastic differential equations with Markovian switching and multiplicative fractional Brownian motion. With the aid of fractional calculus, generalized Riemann-Stieltjes integrals, stopping time techniques and inequality techniques, an averaging principle is established within the framework of Hölder continuous spaces. We prove that the solution of the original fractional Markovian jump system converges in the mean-square sense to that of the averaged equation, thereby justifying the averaging method as an effective technique for reducing the system’s complexity. Finally, concrete examples are presented to demonstrate our theoretical findings. Full article

Institutional distrust is treated here not as a low value of trust but as a positive social disposition, the settled expectation that formal procedures and official explanations no longer carry their stated public meaning. The paper studies the consolidation of that disposition as a threshold event. Building on a stochastic trust-phase model, it applies the same multiplicative-noise mechanism to a delegitimating assertion, so the bounded state variable is the probability of adopting institutional distrust. A logit transformation maps the inherited nonlinear diffusion exactly onto Brownian motion with drift and yields closed-form first-passage formulas for the crossing of operational distrust thresholds. The endpoints of the bounded variable are limiting consolidated regimes rather than finite-time targets, so observable institutional failure is a threshold passage and not literal absorption at zero trust. The drift-to-turbulence ratio fixes the shape of the crossing probabilities and the noise scale fixes the time scale. The same coordinate measures the distance between social layers facing one assertion. In United States partisan survey data, this inter-layer logit distance is large and, on consolidated assertions, stationary, the empirical signature of a completed passage, while valence assertions reset with the change in incumbent. The empirical section illustrates the coordinate rather than calibrating or validating the dynamics: the drift and turbulence parameters are not estimated, as that would require matched longitudinal items with recorded field dates and published subsample sizes. Full article

Background/Objectives: Laboratory automation is a key strategy for increasing productivity and reducing sample turnaround time (TAT), a common indicator of laboratory performance. However, owing to the statistical distribution of TAT values, conventional descriptors such as mean, standard deviation, and percentiles cannot capture the processing history of individual samples. In this study, sample flow within a highly automated laboratory system was analyzed by analogy with the Brownian motion of molecules in solution, using an ad hoc modified Dynamic Light Scattering (DLS) correlation function. Methods: Seven processing histories, each consisting of 1000 samples and representing different TAT scenarios, were generated, and the corresponding correlation functions were calculated. Each sample was assumed to remain correlated with its initial state (value = 1) until its TAT was reached; thereafter, once the result was produced, the sample was considered uncorrelated and its status value became 0. The correlation function was defined as the normalized progressive sum, over time, of the status values of all analyzed samples at each time point. Results: The DLS-inspired autocorrelation function enabled the derivation of parameters describing both overall system performance and sample processing status. These parameters provide quantitative indicators for near-real-time monitoring of automation chain efficiency and reveal system features that are not accessible through conventional TAT statistics. Conclusions: This approach allows the definition of measurable metrics describing the system’s capacity to buffer and mitigate operational disruptions at both the global and individual-sample levels. The proposed framework provides a novel tool for evaluating, monitoring, and comparing the performance of laboratory automation systems. Full article

The temporal course of neuronal electric activity within brain networks, or neurodynamics, reflects the structural and functional properties of the neuronal populations that generate it. Using intracranial stereo-electroencephalography (sEEG) recordings from the public Montreal Neurological Institute (MNI) atlas, we investigated neurodynamics in the primary motor (M1), somatosensory (S1), and auditory (A1) cortices. We tested whether modifying the Higuchi fractal dimension (HFD) by replacing the Euclidean distance with the Fréchet distance could improve sensitivity to local neurodynamics by incorporating trajectory-based similarities in signal evolution. Using a conservative within-subject approach established in the previous literature, we compared signals recorded from different cortical areas within the same individuals (M1 vs. S1: # of people = 16; M1 vs. A1: # = 9; S1 vs. A1: # = 6). To delve deeper into the new measure’s meaning, it was tested on sequences with known fractal properties, the Brownian motion and the Weierstrass function. Results showed that the newly introduced Fréchet-based HFD (HFDf), similarly to standard HFD, consistently discriminated cortical areas at the intra-subject level, confirming the robustness of fractal dimension as a descriptor of region-specific neurodynamics. Contrary to our hypothesis, HFDf did not provide additional sensitivity across areas and notably, it displayed less evident reduction of values in sleep than awake. While cortical regions may share common governing principles across spatiotemporal scales, these do not necessarily translate into strict similarity in temporal signal morphology. We suggest that these findings support that the free-scale nature of neurodynamics is not a self-similar one. This refinement of quantitative tools for cortical neurodynamic mapping paves the way towards novel tools for neuroimaging-informed neuromodulation strategies. Full article

We present the first application of the Multifractal Model of Asset Returns (MMAR) to an implied volatility index, using 36 years of daily CBOE VIX observations spanning four economic cycles. Three general conclusions emerge. First, implied volatility is multifractal: its scaling function is strictly concave, and this curvature survives explicit comparison against monofractal, ARMA, and ARFIMA nulls fitted to the same data, so it cannot be reproduced by anti-persistence or short-range linear dependence alone. Second, unlike equity price indices which are persistent, the VIX is strongly subdiffusive ($\widehat{H}\approx 0.18$, far below $\frac{1}{2}$), which is the multifractal signature of its mean-reverting character; the lognormal cascade is nonetheless admissible, so the construction is internally consistent. Third, admissibility notwithstanding, the lognormal cascade is insufficient in the extreme tails. Across Monte Carlo validation, higher-moment and tail-risk (VaR/ES) comparisons, and a GARCH/EGARCH/FIGARCH benchmark, it captures the bulk of the distribution but systematically underestimates the most violent volatility spikes and does not reproduce VIX’s pronounced positive skewness. We quantify this: the admissible cascade recovers about 84% of the excess kurtosis and reproduces 95–99% Value-at-Risk and 95% Expected Shortfall almost exactly, but it understates the deepest Expected Shortfall, and, being symmetric, it cannot reproduce the positive skew, underpricing far-out-of-the-money option premia by up to 100%. The indicated direction is asymmetric, heavier-tailed cascade extensions. Beyond VIX, the analysis offers a reproducible template for distinguishing genuine multifractality from its linear imitators in any volatility series. Full article

We investigate dynamic weighted fractional information-theoretic measures for linear stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/2,1)$. Motivated by recent constructions of fractional Deng entropy and building upon explicit Gaussian solutions and closed-form fractional moments derived in previous work, we establish fully analytical expressions for the Shannon entropy, Rényi entropy, Tsallis entropy, extropy, and a continuous weighted fractional entropy $\mathbb{E}\left[X_t^p(-\log p_{X_t}\left(X_t\right))\right]$ for $p\ge 0$, expressed directly in terms of known fractional moments without density estimation. All derived measures share a universal asymptotic scaling law growing as $H\log t$, establishing a precise quantitative link between long-memory effects and information dynamics. The weighted fractional entropy further reveals remarkable structural properties as a function of the weighting order p, exposing a dual role of long memory on the system’s informational content. As a concrete application, we characterize anomalous diffusion in aging soft materials through an explicit critical time linking maximal uncertainty to the memory exponent H and the macroscopic aging rate. All results are validated through extensive Monte-Carlo simulations, demonstrating excellent agreement with the closed-form expressions across a wide range of Hurst exponents H and weighting orders p. Full article

The main contribution of this paper is to prove the existence and uniqueness of almost automorphic solutions in distribution for a class of McKean–Vlasov SDEs driven by fractional Brownian motion, under appropriate conditions on the coefficients. The practical relevance of this result is illustrated by analyzing a stochastic heat equation on a bounded domain. Full article

Hybrid carbon nanotube–fullerene architectures provide a controllable setting in which to study irreversibility and information flow in strongly structured quantum environments. We analyze entropy generation in a platform where paramagnetic endohedral fullerenes (PEFs), such as N@C₆₀ and P@C₆₀, are encapsulated inside a suspended carbon nanotube (CNT) resonator, such that selected multi-level PEF spin states define an effective qubit coupled to quantized CNT flexural modes. Motivated by prior work on fullerene-filled CNTs, on spin–phonon manipulation in suspended nanotubes, and on exact phase-space propagators for damped driven oscillators, we formulate a hybrid open-system description that combines a driven quantum Brownian description of the CNT resonator with an effective Jaynes–Cummings type spin–vibrational interaction. The resonator dynamics are represented in phase space through the Wigner function, whose time evolution can be written analytically in terms of the initial Wigner distribution and a Gaussian propagator. This representation makes it possible to separate drive-induced phase space displacement, diffusion, and damping, and to connect these features directly to entropy flow. The coupled spin–mechanical dynamics are then embedded in a Lindblad quantum master equation that includes mechanical damping, spin relaxation, pure dephasing, and thermally activated excitation channels. Within this framework we derive the entropy balance equation—identifying entropy flux and non-negative entropy production—and examine how hybridization between the molecular spin and the nanotube vibration redistributes irreversibility between coherent exchange and dissipative channels. We show that spin–phonon coupling enhanced by a magnetic field gradient, resonant driving, and moderate thermal occupation can produce identifiable crossovers between entropy–production regimes dominated by the oscillator and those dominated by the spin. The resulting framework provides a quantitative basis for using CNT–PEF hybrids as nanoscale platforms for studying nonequilibrium quantum thermodynamics, decoherence, and information loss in structured vibrational environments. Full article

This paper studies Dirichlet problems for one-dimensional Lévy-type nonlocal elliptic equations on the half-line. The equation $L^{\mu }\nu (x)=f(x),x>0,\nu (x)=0,x\le 0$ is transformed into a weighted nonlocal equation associated with a multiplicative jump process. Under basic structural assumptions on the Lévy measure, the transformed generator is realized through a martingale problem, and the associated exponential killing representation gives a probabilistic mild solution with an immediate $L^{\infty }$-estimate. For the one-dimensional fractional Laplacian, the transformed process is exactly multiplicative. This yields a new approach in which solution estimates are derived from the stochastic equation of the transformed process; smooth-data resolvent solutions are estimated in weighted $L_p$-spaces and extended to general data by approximation. For more general Lévy measures, a smooth weighted energy estimate is proved. The key analytic input is a weighted adjoint integral inequality for the transformed generator, verified for subordinate Brownian motions associated with Bernstein functions and for non-unimodal logarithmically perturbed stable-type operators. Full article

This study investigates the growth and evolution of SiO₂-based inclusions in Si-killed steel under stagnant conditions and varying oxygen levels. Deoxidation experiments were conducted in a high-temperature furnace using commercial FeSi, with systematic variations in holding time and total oxygen content. Automated SEM–EDS analysis was employed to quantify inclusion size, number density, and chemical composition. Under stagnant conditions, SiO₂ inclusions were observed to grow and coarsen in the absence of melt agitation, following a t^1/3 scaling law. In high-oxygen melts, rapid inclusion growth was dominated by Stokes collision mechanisms, resulting in the formation of inclusions in the size range of 1–5 μm, which were subsequently removed by flotation. In contrast, low-oxygen melts exhibited slower growth kinetics governed primarily by Brownian motion and Ostwald ripening, producing smaller inclusions with characteristic sizes of 1–2 μm. These results demonstrate that the initial oxygen content plays a decisive role in controlling the dominant growth mechanisms and the extent of inclusion coarsening in non-agitated steel. Full article

This study formulates a corporate abatement decision problem under carbon price uncertainty as a continuous-time stochastic control model. To this end, the carbon price is modeled as a geometric Brownian motion, while abatement capacity is accumulated through costly effort and depreciates over time. Specifically, the firm chooses its abatement effort to maximize expected discounted profits while accounting for allowance purchasing costs, compliance-related penalties, abatement costs, and potential revenues from surplus allowances. The paper contributes by integrating stochastic carbon prices, endogenous abatement-capacity accumulation, allowance-shortage/allowance-surplus asymmetry, and surplus allowance monetization into a unified corporate abatement framework. Applying the dynamic programming principle, the associated Hamilton–Jacobi–Bellman equation is derived, and the bounded optimal abatement effort is characterized in feedback form. Since the resulting nonlinear HJB equation generally does not admit a closed-form solution, a finite-difference scheme with damped policy iteration is used for numerical analysis. The results show that optimal abatement effort is strongly state-dependent. Higher carbon prices strengthen abatement incentives in the allowance-shortage region, whereas effort declines sharply after reaching allowance neutrality if surplus allowances cannot be monetized. Moreover, partial monetization of surplus allowances significantly increases abatement effort in the surplus region and can shift firms’ behavior from passive compliance to active low-carbon investment. Overall, these findings suggest that surplus allowance monetization plays an important role in sustaining firms’ abatement incentives under carbon price uncertainty. Full article

Accurate Remaining Useful Life (RUL) prediction is pivotal for the intelligent operation and maintenance of high-precision equipment. However, existing deep learning-based prognostic methods predominantly focus on point estimations and often overlook the non-Markovian characteristics and stochastic uncertainties inherent in complex mechanical degradation. To bridge this gap, this study proposes a novel uncertainty-aware hybrid prognostic framework by synergizing TCN–Transformer architectures with fractional Brownian motion (FBM). Specifically, a TCN–Transformer hybrid network is developed to adaptively learn a multi-scale drift function, effectively capturing both localized causal features and global long-range temporal dependencies. Concurrently, the FBM component is employed to model the diffusion process, explicitly accounting for the long-range dependence and inherent stochasticity of degradation. By leveraging the first hitting time (FHT) principle, an approximate analytical expression for the RUL probability density function (PDF) is derived based on an established approximation treatment for FBM-driven degradation processes, enabling robust uncertainty quantification. Experimental results on both the XJTU-SY bearing dataset and the servo tool holder power head system dataset demonstrate that the proposed method achieves superior predictive accuracy and reliable uncertainty quantification, thereby providing effective support for condition-based maintenance and intelligent decision-making. Full article

This paper addresses the existence of mild solutions and the approximate controllability of a class of higher-order Hilfer fractional semi-linear neutral stochastic differential equations with non-instantaneous impulses in Hilbert spaces. The system is driven by both fractional Brownian motion and Poisson jumps, thereby capturing long-range dependence as well as random discontinuities. By combining techniques from fractional calculus, stochastic analysis, and operator theory, we establish sufficient conditions for the existence of mild solutions. The analysis is carried out through the construction of suitable solution operator families and the application of Sadovskii’s fixed point theorem in an appropriate phase space framework. In addition, we investigate the controllability properties of the system and derive criteria ensuring approximate controllability of the underlying fractional neutral dynamics. The proposed approach relies on the structural properties of the higher-order Hilfer fractional derivative, estimates for stochastic integrals with respect to fractional Brownian motion, and compactness arguments adapted to non-instantaneous impulsive effects. The inclusion of Poisson jumps and neutral terms introduces significant analytical difficulties, which are overcome using refined resolvent operator techniques and fractional power estimates. An illustrative example is presented to demonstrate the applicability of the theoretical results. The results obtained generalize and unify several recent developments in the theory of fractional stochastic systems and provide a flexible framework for analyzing controlled dynamical models with memory, randomness, and impulsive behavior. Full article

Significance: This study addresses critical industrial and biomedical applications including glass blowing (thermal management of shrinking sheets), polymer sheet extrusion (controlled cooling), magnetic drug delivery (nanoparticle targeting), and nuclear reactor cooling (enhanced heat transfer). Aim: We present a novel nonlinear analysis of magnetohydrodynamic (MHD) boundary layer flow of a Jeffery Al₂O₃ nanofluid over a shrinking permeable plate with convective boundary conditions, uniquely integrating mixed convection, Ohmic dissipation, heat generation, Brownian motion, and thermophoresis within a non-Newtonian nanofluid framework. Methodology: The governing partial differential equations are transformed using similarity transformations and solved via the Adomian decomposition method (ADM). Comprehensive validation against RK4, RK45, and bvp4c demonstrates excellent agreement with maximum relative errors below $5\times {10}^{-4}$. Key Contribution: (i) Normal velocity decreases by 15–25% as the Biot number increases from $Bi=0.4$ to $0.6$; (ii) tangential velocity decreases by 20–30% as the magnetic parameter increases from $M=5$ to 15; (iii) temperature increases by 30–40% as the Eckert number increases from $Ec=0.5$ to $2.5$; (iv) ADM converges within 12–15 terms with $L_2$ errors $<{10}^{-5}$; (v) skin friction coefficient increases from $C_f=3.02713$ to $3.90082$ as $Q_0$ increases from 1 to 4; (vi) Nusselt number values: $Nu/\sqrt{Re}=0.4621$ at $Pr=0.7$, $0.8954$ at $Pr=2$, $3.2890$ at $Pr=20$. These quantitative findings provide design guidelines for engineers in thermal management and biomedical applications. Full article