Evolving privacy: drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP

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• dc.contributor.author Amorino, Chiara
• dc.contributor.author Gloter, Arnaud
• dc.contributor.author Halconruy, Hélène
• dc.date.accessioned 2025-05-07T11:28:26Z
• dc.date.available 2025-05-07T11:28:26Z
• dc.date.issued 2025
• dc.date.updated 2025-05-07T11:28:26Z
• dc.description.abstract The problem of estimating a parameter in the drift coefficient is addressed for N discretely observed independent and identically distributed stochastic differential equations (SDEs). This is done considering additional constraints, wherein only public data can be published and used for inference. The concept of local differential privacy (LDP) is formally introduced for a system of stochastic differential equations. The objective is to estimate the drift parameter by proposing a contrast function based on a pseudo-likelihood approach. A suitably scaled Laplace noise is incorporated to meet the privacy requirements. Our key findings encompass the derivation of explicit conditions tied to the privacy level. Under these conditions, we establish the consistency and asymptotic normality of the associated estimator. Notably, the convergence rate is intricately linked to the privacy level, and in some situations may be completely different from the case where privacy constraints are ignored. Our results hold true as the discretization step approaches zero and the number of processes N tends to infinity.
• dc.format.mimetype application/pdf
• dc.identifier.citation Amorino C, Gloter A, Halconruy H. Evolving privacy: drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP. Stoch Process Their Appl. 2025 Mar;181:104557. DOI: 10.1016/j.spa.2024.104557
• dc.identifier.doi http://dx.doi.org/10.1016/j.spa.2024.104557
• dc.identifier.issn 0304-4149
• dc.identifier.uri http://hdl.handle.net/10230/70319
• dc.language.iso eng
• dc.publisher Elsevier
• dc.relation.ispartof Stochastic Processes and their Applications. 2025 Mar;181:104557
• dc.rights © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Local differential privacy
• dc.subject.keyword Parameter drift estimation
• dc.subject.keyword High frequency data
• dc.subject.keyword Convergence rate
• dc.subject.keyword Privacy for processes
• dc.title Evolving privacy: drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion