Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching by Hua Yang, Feng Jiang

“…We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs). …”
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Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control by Fathalla A. Rihan, Chinnathambi Rajivganthi, Palanisamy Muthukumar

“…In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. …”
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About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps by Leonid Shaikhet

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Controlled Filtered Poisson Processes by Mario Lefebvre

“…Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. …”
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Jump Diffusion Modelling for the Brazilian Short-Term Interest Rate by José Carlos Nogueira Cavalcante Filho, Edson Daniel Lopes Gonçalves

“…In order to capture the informational effect of the Brazilian short-term interest rate (SELIC rate) by Poisson jumps, we build on the tests condu cted by Das (2002) and Johannes (2004), which show the significance of such structures for U.S. …”
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Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps by ZaiTang Huang, ChunTao Chen

“…Interestingly, this shows the effect of the Poisson noise which can stabilize or unstabilize the system which is significantly different from the classical Brownian motion process.…”
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A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution by D. P. Siu, G. S. Ladde

“…The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the systems are obtained. …”
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Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump by Yong Xu, Ruifang Wang

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Stochastic θ-Methods for a Class of Jump-Diffusion Stochastic Pantograph Equations with Random Magnitude by Hua Yang, Feng Jiang

“…This paper is concerned with the convergence of stochastic θ-methods for stochastic pantograph equations with Poisson-driven jumps of random magnitude. The strong order of the convergence of the numerical method is given, and the convergence of the numerical method is obtained. …”
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Optimal Trade Execution under Jump Diffusion Process: A Mean-VaR Approach by Tianmin Zhou, Can Jia, Handong Li

“…The jumps in our model are described by the compound Poisson process where random jump amplitude depicts the information impact on price process. …”
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Inflation Volatility and Growth in a Stochastic Small Open Economy: A Mixed Jump-Diffusion Approach by Isela Téllez-León, Francisco Venegas-Martínez, Abigail Rodríguez-Nava

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Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion by Lin Hu, Siqing Gan

“…A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes. A general framework for mean-square convergence of the methods is provided. …”
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Three new species of the spider genus Naphrys Edwards (Araneae, Salticidae) under morphology and molecular data with notes in the distribution of Naphrys acerba (Peckham & Peckham)... by Juan Maldonado-Carrizales, Alejandro Valdez-Mondragón, María L. Jiménez-Jiménez, Javier Ponce-Saavedra

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