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As a concrete setting where stochastic partial differential equations (SPDEs) are able to model real phenomena, we propose a stochastic Meinhardt model for cell repolarisation 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.
In this work we study a class of stochastic processes ${X_t}_{tinN}$, where $X_t = (phi circ T_s^t)(X_0)$ is obtained from the iterations of the transformation T_s, invariant for an ergodic probability mu_s on [0,1] and a continuous by part function
This work contributes to the limited literature on estimating the diffusivity or drift coefficient of nonlinear SPDEs driven by additive noise. Assuming that the solution is measured locally in space and over a finite time interval, we show that the
Goods formula and Fishers method are frequently used for combining independent P-values. Interestingly, the equivalent of Goods formula already emerged in 1910 and mathematical expressions relevant to even more general situations have been repeatedly
We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams. We develop a novel estimator that relies on kernel smoothing to pre-process the pairwise comparis
Ageing of lithium-ion batteries results in irreversible reduction in performance. Intrinsic variability between cells, caused by manufacturing differences, occurs throughout life and increases with age. Researchers need to know the minimum number of