Mean reflected stochastic differential equations with jumps

Briand, Phillippe; Ghannoum, Abir; Labart, Céline

doi:10.1017/apr.2020.11

Cited by 11 publications

(4 citation statements)

References 28 publications

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“…Similar [1] and [22], the previous system of interacting particles can be seen as a multidimensional reflected SDE with oblique reflection. If h is concave, the set…”

Section: Propagation Of Chaosmentioning

confidence: 94%

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Mean reflected Mckean-Vlasov stochastic differential equation

Liu¹,

Shaopeng²

2023

Preprint

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In this paper, we investigate a class of mean reflected McKean-Vlasov stochastic differential equation, which extends the equation proposed by [1] by allowing the solution's distribution to not only constrain its behavior, but also affect the diffusion and drift coefficients. We establish the existence and uniqueness results of this class, investigate the propagation of chaos, and examine the stability properties with respect to the initial condition, coefficients, and driving process. Moreover, we provide a rigorous proof of a Fredlin-Wentzell type large deviations principle using the weak convergence method. We also demonstrate the existence of an invariant measure and employ the coupling by change of measure method to prove log-Harnack inequality and shift Harnack inequality. Our study sheds light on the properties and behaviors of these reflected Mckean-Vlasov stochastic differential equation and contributes to the ongoing research in this field.

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“…Similar [1] and [22], the previous system of interacting particles can be seen as a multidimensional reflected SDE with oblique reflection. If h is concave, the set…”

Section: Propagation Of Chaosmentioning

confidence: 94%

“…They also proposed a numerical simulation method based on particle approximation techniques. [22] extended this work to Lévy driven MR-SDE. [23] examined the MR-SDE with two reflective walls and solved the Skorokhod problem with the mean minimum condition.…”

Section: Introductionmentioning

confidence: 94%

Mean reflected Mckean-Vlasov stochastic differential equation

Liu¹,

Shaopeng²

2023

Preprint

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“…Some authors research were carefully studied to establish links between the Wiener process, Poisson Jumps and the differential equation that form the SDEs; few of the authors are Higham and Kloeden P. E. (2000) [11], Lamba, Mattingly and Stuart (2006) [16], Bayram, Partal and Byukoz(2018) [4] and Briand, Labart and Ghannoum (2018) [5]. The work of these authors was studied for the possibility of developing new methods in next chapters.…”

Section: 3 Stochastic Differential Equationmentioning

confidence: 99%

Euler-Maruyama Approximation of Stochastic Dependent Poisson-Jump in Black-Scholes Asset Price Model

Kayode,

Abejide

2023

Theoretical Mathematics &Amp; Applications

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In this study, the Gaussian white noise and the differential Poisson of the Stochastic Differential Equation(SDE) with distributed jump are examined. Using Ito integral as a tool, a one step Euler-Maruyama (E-M) method is considered for the approximation of Stochastic Dependent Poisson Analysis (SDPA) in finance. The Deterministic Quadrature Rule (DQR) was used in the establishment of the method for easy examination of the Black-Scholes asset price model for stock investors; MATLAB package was used for simulation of the method. However the Mean Absolute Error (MAE) as well as Strong Order of Convergence (SOC) method was considered to ascertain its usability. The result clearly shows entry points and exit points of stock market. Consequently, the findings of this research is strongly recommended. Keywords: Euler-Maruyama method, Stochastic differential equation, Ito integral, Poisson distributed jump, Random variables, Deterministic model.

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“…The boundary conditions can be, for example, reflecting, absorbing or even mixed boundary conditions. Recent developments reported in [5,7] bring us to the study of a system of Skorokhod-type SDEs modelling the interactions between active and passive populations. Many important operations research problems, including those arising in queueing theory, require the models describing reflecting stochastic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Combining Coupled Skorokhod SDE and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

Thieu¹,

Melnik²

2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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To model reliably behavioral systems with complex bio-social interactions, accounting for uncertainty quantification, is critical for many application areas. However, in terms of the mathematical formulation of the corresponding problems, one of the major challenges is coming from the fact that corresponding stochastic processes should, in most cases, be considered in bounded domains, possibly with obstacles. This has been known for a long time and yet, very little has been done for the quantification of uncertainties in modelling complex behavioral systems described by such stochastic processes. In this paper, we address this challenge by considering a coupled system of Skorokhodtype stochastic differential equations (SDEs) describing interactions between active and passive participants of a mixed-population group. In developing a multi-fidelity modelling methodology for such behavioral systems, we combine low-and high-fidelity results obtained from (a) the solution of the underlying coupled system of SDEs and (b) simulations with a statistical-mechanics-based lattice gas model, where we employ a kinetic Monte Carlo procedure. Furthermore, we provide representative numerical examples of healthcare systems, subject to an epidemic, where the main focus in our considerations is given to an interacting particle system of asymptomatic and susceptible populations.

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Mean reflected stochastic differential equations with jumps

Cited by 11 publications

References 28 publications

Mean reflected Mckean-Vlasov stochastic differential equation

Mean reflected Mckean-Vlasov stochastic differential equation

Euler-Maruyama Approximation of Stochastic Dependent Poisson-Jump in Black-Scholes Asset Price Model

Combining Coupled Skorokhod SDE and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

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