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Mathematics > Statistics Theory

arXiv:2210.08800 (math)
[Submitted on 17 Oct 2022]

Title:Parametric estimation of stochastic differential equations via online gradient descent

Authors:Shogo Nakakita
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Abstract:We propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the estimators over a family of stochastic differential equations. The derivation of the bounds involves three underlying theoretical results: the analysis of the stochastic mirror descent algorithm based on dependent and biased subgradients, the simultaneous exponential ergodicity of classes of diffusion processes, and the proposal of loss functions whose approximated stochastic subgradients are dependent only on the known model and observations.
Subjects: Statistics Theory (math.ST); Optimization and Control (math.OC); Probability (math.PR)
MSC classes: 62M05 (Primary) 37A25, 60J60, 62L12, 90C25 (Secondary)
Cite as: arXiv:2210.08800 [math.ST]
  (or arXiv:2210.08800v1 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2210.08800

Submission history

From: Shogo Nakakita [view email]
[v1] Mon, 17 Oct 2022 07:31:37 UTC (42 KB)
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