Recursive computation of the invariant measure of a stochastic differential equation driven by a L\'evy process [PDF]
, 2008 We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process.
A Lévy Process +2 more
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Logarithmic Lévy process directed by Poisson subordinator
Modern Stochastics: Theory and Applications, 2019 Let $\{L(t),t\ge 0\}$ be a Lévy process with representative random variable $L(1)$ defined by the infinitely divisible logarithmic series distribution. We study here the transition probability and Lévy measure of this process.
Penka Mayster, Assen Tchorbadjieff
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A Novel Ant Colony Optimization Algorithm With Levy Flight
IEEE Access, 2020 Ant Colony Optimization (ACO) is a widely applied meta-heuristic algorithm. Little researches focused on the candidate selection mechanism, which was developed based on the simple uniform distribution.
Yahui Liu, Buyang Cao
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On occupation time for on-off processes with multiple off-states
Modern Stochastics: Theory and Applications, 2022 The need to model a Markov renewal on-off process with multiple off-states arise in many applications such as economics, physics, and engineering. Characterization of the occupation time of one specific off-state marginally or two off-states jointly is ...
Chaoran Hu, Vladimir Pozdnyakov, Jun Yan
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A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes [PDF]
, 2016 We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We
Arratia Quesada, Argimiro Alejandro +2 more
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Derivation of the Fractional Fokker–Planck Equation for Stable Lévy with Financial Applications
Mathematics, 2023 This paper aims to propose a generalized fractional Fokker–Planck equation based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion.
Reem Abdullah Aljethi, Adem Kılıçman
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Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion
Physical Review Research, 2020 Strong anomalous diffusion phenomena are often observed in complex physical and biological systems, which are characterized by the nonlinear spectrum of exponents qν(q) by measuring the absolute qth moment 〈|x|^{q}〉.
Xudong Wang, Yao Chen, Weihua Deng
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Investigating Levy's model in financial series prediction(case of vanilla option) [PDF]
Mathematics and Modeling in FinanceIn recent years, there has been growing interest in the application of stochastic processes to model financial markets, particularly in the pricing and prediction of derivative instruments such as options. One of the more advanced models that has emerged
Seyed Jalal Tabatabaei
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Stylized Model of Lévy Process in Risk Estimation
Mathematics, 2023 Risk management is a popular and important problem in academia and industry. From a small-scale system, such as city logistics, to a large-scale system, such as the supply chain of a global industrial or financial system, efficient risk management is ...
Xin Yun +4 more
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Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises
Abstract and Applied Analysis, 2013 This paper is devoted to the investigation of random dynamics of the stochastic Boussinesq equations driven by Lévy noise. Some fundamental properties of a subordinator Lévy process and the stochastic integral with respect to a Lévy process are discussed,
Jianhua Huang, Yuhong Li, Jinqiao Duan
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