Maximal speed of particles in super-Lévy process

We introduce a super-Lévy process and study maximal speed of all particles in the range and the support of the super-Lévy process. The state of historical super-Lévy process is a measure on the set of paths. We study the maximal speed of all particles during a given time period, which turns out to be a function of the packing dimension of the time period. We calculate the Hausdorff dimension of the set of a-fast paths in the support and the range of the historical super-Lévy process.

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

ASYMPTOTICS OF THE SOLUTIONS TO STOCHASTIC WAVE EQUATIONS DRIVEN BY A NON-GAUSSIAN LéVY PROCESS

In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Levy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.

A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation

This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)^(n)X_(i)Y_(i),1/α√n∑_(i=1)^(n)X_(i))}_(n=1)^(∞)converges in distribution to L_(1),where L_(t=(ε_(t),η_(t),ζ_(t))),t∈[0,1],is a multidimensional nonlinear Lévy process with an uncertainty■set as a set of Lévy triplets.This nonlinear Lévy process is characterized by a fully nonlinear and possibly degenerate partial integro-differential equation(PIDE){δ_(t)u(t,x,y,z)-sup_(F_(μ),q,Q)∈■{∫_(R^(d)δλu(t,x,y,z)(dλ)with.To construct the limit process,we develop a novel weak convergence approach based on the notions of tightness and weak compactness on a sublinear expectation space.We further prove a new type of Lévy-Khintchine representation formula to characterize.As a byproduct,we also provide a probabilistic approach to prove the existence of the above fully nonlinear degenerate PIDE.

Option Pricing Model Driven by G-Lévy Process under the G-Expectation Framework

In this paper, we first present an option pricing model of stochastic differential equations driven by the G-Lévy process under the G-expectation framework, and prove the generalized Black-Scholes equations. Then, we present the algorithm for the time-homogeneous Poisson process versus the non-time-homogeneous Poisson process. Finally, we provide an explicit solution of generalized Black-Scholes equations and simulate it numerically with Matlab software.

基于混沌精英和Lévy飞行策略的鲸鱼优化算法

针对鲸鱼优化算法(Whale Optimization Algorithm,WOA)存在的收敛速度慢、精度低的问题,提出了基于Tent混沌精英和Lévy飞行策略的鲸鱼优化算法(TELWOA)。使用Tent混沌映射初始化鲸鱼种群,保持种群的多样性,并通过引入精英反向学习策略,对初始种群的精英个体生成反向解,选取适应度高的种群作为下一代鲸鱼种群,加快算法收敛速度。其次,通过使用非线性收敛因子,缓解算法全局搜索和局部搜索能力不平衡的现象。最后,在鲸鱼位置寻优过程中使用Lévy飞行策略,避免算法陷入局部最优,提升算法的全局搜索能力。通过对不同改进策略的有效性分析、与其他智能算法的对比分析,证明了TELWOA算法在收敛精度、算法稳定性和全局寻优能力上与对比算法有显著提升,具有一定的实际工程应用能力。

融合学习差异与Lévy飞行的动态平衡正余弦算法

为了提升正余弦算法的收敛性能,本文提出一种融合学习差异与Lévy飞行的动态平衡正余弦改进算法,定义为SCALLD算法。通过引入学习差异策略,减少搜索个体对其位置信息的依赖,增强全局探索能力;加入Lévy飞行机制,丰富种群多样性,提升探索能力;采用动态平衡策略,平衡探索与开发能力,提高收敛速度和稳定性。在CEC2022基准测试函数上的实验表明,与六种算法相比,SCALLD展现出更优的收敛性能和稳定性,Wilcoxon秩和检验进一步证明了SCALLD的竞争优势,为解决复杂优化问题提供参考。

由Lévy过程驱动的加权自排斥扩散的长时间行为和统计推断

假设是一个跳有界且界限为1的Lévy过程,生成三元组为。在本文中,我们考虑了由Lévy过程驱动的线性自排斥扩散方程,其中,和。这类过程是一类自交互扩散过程。我们研究了当t趋于无穷时解的长时间行为,发现它具有一种循环收敛性,这在此前的研究中尚未有类似的结论。进一步的,当w=0时在连续观测情况下,通过最小二乘法给出了方程参数的估计。我们证明了的估计量具有强相合性,并讨论了它的渐近分布。

Symmetric Brownian motor subjected to Lévy noise

In the past few years,attention has mainly been focused on the symmetric Brownian motor(BM)with Gaussian noises,whose current and energy conversion efficiency are very low.Here,we investigate the operating performance of the symmetric BM subjected to Lévy noise.Through numerical simulations,it is found that the operating performance of the motor can be greatly improved in asymmetric Lévy noise.Without any load,the Lévy noises with smaller stable indexes can let the motor give rise to a much greater current.With a load,the energy conversion efficiency of the motor can be enhanced by adjusting the stable indexes of the Lévy noises with symmetry breaking.The results of this research are of great significance for opening up BM’s intrinsic physical mechanism and promoting the development of nanotechnology.

Identifying influential spreaders in social networks: A two-stage quantum-behaved particle swarm optimization with Lévy flight

The influence maximization problem aims to select a small set of influential nodes, termed a seed set, to maximize their influence coverage in social networks. Although the methods that are based on a greedy strategy can obtain good accuracy, they come at the cost of enormous computational time, and are therefore not applicable to practical scenarios in large-scale networks. In addition, the centrality heuristic algorithms that are based on network topology can be completed in relatively less time. However, they tend to fail to achieve satisfactory results because of drawbacks such as overlapped influence spread. In this work, we propose a discrete two-stage metaheuristic optimization combining quantum-behaved particle swarm optimization with Lévy flight to identify a set of the most influential spreaders. According to the framework,first, the particles in the population are tasked to conduct an exploration in the global solution space to eventually converge to an acceptable solution through the crossover and replacement operations. Second, the Lévy flight mechanism is used to perform a wandering walk on the optimal candidate solution in the population to exploit the potentially unidentified influential nodes in the network. Experiments on six real-world social networks show that the proposed algorithm achieves more satisfactory results when compared to other well-known algorithms.

Lévy噪声和高斯白噪声驱动的非对称三稳系统的相转移问题研究

讨论了非对称三稳系统在Lévy噪声和高斯白噪声共同驱动下的相转移问题。采用四阶Runge-Kutta算法,计算了系统的稳态概率密度函数,通过改变系统参数和噪声参数观察其稳态概率密度函数曲线形态的变化情况。研究发现,非对称参数、加性噪声强度、乘性噪声强度、稳定性指标、偏斜参数均可诱导系统相转移,当分别改变加性噪声强度和乘性噪声强度时,概率密度函数的峰数与高度的变化情况相反。此外,在相同的非对称参数下,随着偏斜参数正负取值的变化,概率密度曲线图中峰的结构亦呈现不同的现象。

具有Lévy跳的随机时滞食饵-捕食模型的最优收获

研究了一类带Lévy跳的时滞食饵-捕食模型的捕捞策略.利用比较原理分析物种平均持久性和灭绝性的充分条件,在一定假设条件下证明了该模型分布的稳定性,运用遍历法建立最优收获策略存在的条件,得到了最优捕捞努力量和最大持续产量.最后通过数值模拟验证理论结果.

乘性Lévy噪声驱动的随机传染病模型参数估计

利用最小二乘方法研究由乘性Lévy噪声驱动的随机易感潜伏—感染-治愈-易感(susceptible exposed-infectious-recovered-susceptible,SEIRS)传染病模型的参数估计问题.首先,基于模型的离散观测样本,得到模型中未知参数的最小二乘估计量;其次,讨论当噪声强度趋于0且离散观测样本量趋于无穷时估计量的渐近一致性,并给出估计量的极限分布;最后,选定不同的噪声强度和样本量进行数值模拟.结果表明:参数估计量的相对误差随样本量增多或噪声强度减小而不断降低,当样本量足够大且噪声强度足够小时估计量几乎接近真实值.

Optimization and Characterization of Combined Degumming Process of Typha angustata L. Stem Fibers

Plant derived natural fibers have been widely investigated as alternatives to synthetic fibers in reinforcing polymers.Researchers over the years have explored many plant fibers using different extraction processes to study their physical,chemical,and mechanical properties.In this context,the present study relates to the extraction,characterization,and optimization of Typha angustata L.stem fibers.For this purpose,desirability functions and response surface methodology were applied to simultaneously optimize the diameter(D),linear density(LD);yield(Y),lignin fraction(L),and tenacity(T)of Typha stem fibers.Typha stems have been subjected to both alkali(NaOH)and enzymatic(pectinex ultra-SPL)treatments.Three levels of process variables including enzyme concentration(10,15,and 20 ml/L)and treatment duration(10,15,and 20 days)were used to design the experiments according to the factorial design.Experimental results were examined by analysis of variance and fitted to second order polynomial model using multiple regression analysis.The Derringer’s desirability function released that the values of process variables generating optimized diameter,linear density,yield,lignin ratio and tenacity are 20 ml/L and 20 days for concentration of pectinex ultra-SPL enzyme and treatment duration,respectively.Confirmation was performed and high degree of correlation was found between the experimental and statistical values.Moreover,the morphological structure has been investigated by the scanning electron microscope,showing a crenelated structure of ultimate fiber bundles of cellulose composing the Typha fiber.Compared to Typha stem non-treated fibers(TSNTF),Typha stem combined treated fibers(TSCTF),brings to improve mechanical properties.This change in mechanical properties is affected by modifying the fiber structure showing alpha cellulose of(66.86%)and lignin ratio of(10.83%)with a crystallinity index of(58.47%).

具有Lévy跳跃驱动的Rosenzweig-MacArthur捕食者–食饵模型的渐近行为

本文主要利用随机分析等相关知识,根据进化稳定策略框架对Rosenzweig-MacArthur捕食者–食饵模型进行改进,证明了具有Lévy跳跃驱动的Rosenzweig-MacArthur捕食者–食饵模型解的存在唯一性和随机有界性,并探究了该模型的灭绝性、持久性和平稳分布。

G-Lévy processes under sublinear expectations

We introduce G-Lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations.We then obtain the Lévy-Khintchine formula and the existence for G-Lévy processes.We also introduce G-Poisson processes.

Path independence of the additive functionals for stochastic differential equations driven by G-lévy processes

In this study,we are interested in stochastic differential equations driven by GLévy processes.We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent property,generalizing a few known findings in the literature.The study is ended with many examples.

Lévy飞行的正余弦乌燕鸥混合算法及应用

为解决标准乌燕鸥算法(STOA)易陷入局部最优和收敛速度慢等缺点,提出一种混合正余弦算法(SCA)和Lévy飞行的自适应乌燕鸥算法(SLSTOA)。采用正余弦算法的搜索方式,同时采用非线性递减自适应正弦因子,改进乌燕鸥算法的攻击搜索方式,来增强STOA算法的全局与局部探索能力。乌燕鸥个体和最优个体通过Lévy飞行策略进行变异,来增加种群多样性和扩大搜索空间,以达到提高跳出局部最优和全局探索能力。与四种先进的元启发式算法比较,SLSTOA算法性能通过6个基准测试函数进行评价,结果表明,相比其他四种元启发式算法,SLSTOA算法精度高、稳定性好和鲁棒性强。同时为验证SLSTOA算法的科学性与实用性,将其应用于解决32t/22.5m桥式起重机主梁结构优化设计中。

A Mean-Field Optimal Control for Fully Coupled Forward-Backward Stochastic Control Systems with Lévy Processes

This paper is concerned with a class of mean-field type stochastic optimal control systems,which are governed by fully coupled mean-field forward-backward stochastic differential equations with Teugels martingales associated to Lévy processes.In these systems,the coefficients contain not only the state processes but also their marginal distribution,and the cost function is of mean-field type as well.The necessary and sufficient conditions for such optimal problems are obtained.Furthermore,the applications to the linear quadratic stochastic optimization control problem are investigated.

Black-Scholes Model under G-Lévy Process

In this paper, we study the option price theory of stochastic differential equations under G-Lévy process. By using G-Itô formula and G-expectation property, we give the proof of Black-Scholes equations (Integro-PDE) under G-Lévy process. Finally, we give the simulation of G-Lévy process and the explicit solution of Black-Scholes under G-Lévy process.