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research-article

Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs

Published: 25 September 2024 Publication History

Abstract

We present a novel deep-learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.

Highlights

Novel deep learning application in multivariate regression and SDEs.
Theoretical support and experimental validation.
Potential impact across various scientific and engineering fields.

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Information & Contributors

Information

Published In

cover image Applied Mathematics and Computation
Applied Mathematics and Computation  Volume 480, Issue C
Nov 2024
286 pages

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 25 September 2024

Author Tags

  1. 65C30
  2. 68Q25

Author Tags

  1. Stochastic differential equations
  2. Markov models
  3. Multivariate regression
  4. Artificial neural networks
  5. Deep learning
  6. Quasi-likelihood function
  7. Maximum likelihood

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