Abstract

As a concrete setting where stochastic partial differential equations (SPDEs) are able to model real phenomena, we propose a stochastic Meinhardt model for cell repolarization and study how parameter estimation techniques developed for simple linear SPDE models apply in this situation. We establish the existence of mild SPDE solutions, and we investigate the impact of the driving noise process on pattern formation in the solution. We then pursue estimation of the diffusion term and show asymptotic normality for our estimator as the space resolution becomes finer. The finite sample performance is investigated for synthetic and real data.

Keywords

  1. local measurements
  2. stochastic partial differential equation
  3. pattern formation
  4. Meinhardt model
  5. stochastic reaction-diffusion equation
  6. drift estimation
  7. augmented MLE

MSC codes

  1. Primary
  2. 60H15
  3. 92C37
  4. 62M05; Secondary
  5. 60J60

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Information & Authors

Information

Published In

cover image SIAM/ASA Journal on Uncertainty Quantification
SIAM/ASA Journal on Uncertainty Quantification
Pages: 179 - 199
ISSN (online): 2166-2525

History

Submitted: 13 October 2020
Accepted: 14 September 2021
Published online: 7 February 2022

Keywords

  1. local measurements
  2. stochastic partial differential equation
  3. pattern formation
  4. Meinhardt model
  5. stochastic reaction-diffusion equation
  6. drift estimation
  7. augmented MLE

MSC codes

  1. Primary
  2. 60H15
  3. 92C37
  4. 62M05; Secondary
  5. 60J60

Authors

Affiliations

Funding Information

Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : SFB1294/1-318763901

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