Asymptotically Periodic Solution of a Stochastic Differential Equation

Manou-Abi, Solym Mawaki; Dimbour, William

doi:10.1007/s40840-019-00717-9

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…• If f and g have at most linear growth it is proved in [15] that there exists a weak solution for α ∈ (1, 2) for which pathwise uniqueness holds whenever the function g is particularly Hölder continuous with exponent lying in [1 − 1 α , 1 α ]. For more recent existence conditions, we refer to [37] and references therein. The Nadaraya-Watson (N-W) estimator is a classical method to estimate the drift function f .…”

Section: Non Parametric Estimation Of the Drift Functionmentioning

confidence: 99%

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Parameter Estimation for a Class of Stable Driven Stochastic Differential Equations

Manou-Abi

2023

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In this paper, we consider parameter estimation for a stochastic process observed at some discrete times that is a solution of a given class of stochastic differential equations driven by α-stable processes, α ∈ (1, 2). Firstly, we consider the diffusion coefficients parameters estimation problem such as the scaling parameter and the driving stable process parameters. Secondly, we address the question of the joint estimation with the drift coefficients for Stable driven Cox–Ingersoll–Ross and Ornstein-Uhlenbeck processes. Our methodology which is based on the use of Nadaraya-Watson estimator is new according to the literature of such estimation problem. Indeed it is based on a combination of the characteristic sample function and the (linear or weighted) regression methods. We discuss the validity and efficiency of the numeric implementation of the estimators on synthetic data and real financial data as indexes and exchange rates. As a forthcoming work, we intend to provide a package (in the R programming language) for this type of estimation problem.

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Section: Non Parametric Estimation Of the Drift Functionmentioning

confidence: 99%

“…When the drift term f is Hölder continuous of order lying in (2 − α, 1) and g is Lipshitz continuous and bounded, then existence and uniqueness of a strong solution is derived in [39], [42]. For more recent existence conditions, we refer to [37] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for a Class of Stable Driven Stochastic Differential Equations

Manou-Abi

2023

Preprint

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Analysis of the COVID-19 epidemic in french overseas department Mayotte based on a modified deterministic and stochastic SEIR model

Manou-Abi

Balicchi

2020

Preprint

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In order to anticipate a future trends in the development of the novel coronavirus COVID-19 epidemic started early at march 13, in the french overseas department Mayotte, we consider in this paper a modified deterministic and stochastic epidemic model. The model divides the total population into several possible states or compartment : susceptible (S), exposed (E) infected and being under an incubation period, infected (I) being infectious, simple or mild removed R M , severe removed (including hospitalized) R S and death cases (D). The adding of the two new compartment R M and R S are driven by data which together replace the original R compartment in the classical SEIR model. We first fit the constant transmission rate parameter to the epidemic data in Mayotte during an early exponential growth phase using an algorithm with a package of the software R and based on a Maximum Likewood estimator. This allows us to predict the epidemic without any control in order to understand how the control measure and public policies designed are having the desired impact of controlling the epidemic. To do this, we introduce a temporally varying decreasing transmission rate parameter with a control or quarantine parameter q. Then we pointed out some values of q to maintain control which is critical in Mayotte given the fragility of its health infrastructure and the significant fraction of the population without access to water.

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