Drift estimation for stochastic reaction-diffusion systems

Pasemann, Gregor; Stannat, Wilhelm

doi:10.1214/19-ejs1665

Cited by 18 publications

(18 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…for Y ∈ H s . In order to control the regularity of X , we apply a splitting argument (see also Cialenco and Glatt-Holtz 2011;Pasemann and Stannat 2020;Altmeyer et al 2020b) and write X = X + X , where X is the solution to the linear SPDE dX t = θ 0 X t dt + BdW t , X 0 = 0, (…”

Section: Basic Regularity Resultsmentioning

confidence: 99%

“…Proof By means of the decomposition ( 22), we proceed as in Pasemann and Stannat (2020). Denote byθ full,N 0 the estimator which is given by ( 21) if theθ N 1 , .…”

Section: Proofmentioning

confidence: 99%

“…A usual choice for Y is a reweighted spectral cutoff of X , which leads to the spectral approach described below. Under additional model assumptions, e.g., if (1) is in fact a stochastic partial differential equation (SPDE) driven by Gaussian white noise, a rather developed parameter estimation theory for θ 0 has been established in Pasemann and Stannat (2020) on the basis of maximum likelihood estimation (MLE).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Diffusivity Estimation for Activator–Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton

et al. 2021

Self Cite

View full text Add to dashboard Cite

A theory for diffusivity estimation for spatially extended activator–inhibitor dynamics modeling the evolution of intracellular signaling networks is developed in the mathematical framework of stochastic reaction–diffusion systems. In order to account for model uncertainties, we extend the results for parameter estimation for semilinear stochastic partial differential equations, as developed in Pasemann and Stannat (Electron J Stat 14(1):547–579, 2020), to the problem of joint estimation of diffusivity and parametrized reaction terms. Our theoretical findings are applied to the estimation of effective diffusivity of signaling components contributing to intracellular dynamics of the actin cytoskeleton in the model organism Dictyostelium discoideum.

show abstract

Section: Basic Regularity Resultsmentioning

confidence: 99%

“…Proof By means of the decomposition ( 22), we proceed as in Pasemann and Stannat (2020). Denote byθ full,N 0 the estimator which is given by ( 21) if theθ N 1 , .…”

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Diffusivity Estimation for Activator–Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…We present several types of semilinear SPDEs whose nonlinearity F satisfies (5.5), which in particular guarantees that all results from this section hold for the solutions to these classes of equations. For technical details see [PS20,ACP20]. 1) (fractional) Heat equation: In the case F = 0, (5.1) becomes linear, sometimes called fractional head equation, and (5.5) is trivially satisfied for any η > 0.…”

Section: Semilinear Spdes On a Bounded Domainmentioning

confidence: 99%

Statistical analysis of discretely sampled semilinear SPDEs: a power variation approach

Cialenco¹,

Kim²,

Pasemann³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are proved by using the notion of ∆-power variations, introduced herein, along with the Hölder-Zygmund norms. Consequently, we prove a new central limit theorem for ∆-power variations of the iterated integrals of a fractional Brownian motion (fBm). These abstract results, besides being of independent interest, in the second part of the paper are applied to estimation of the drift and volatility coefficients of semilinear stochastic partial differential equations in dimension one, driven by an additive Gaussian noise white in time and possibly colored in space. In particular, we solve the earlier conjecture from [CKL20] about existence of a nontrivial bias in the estimators derived by naive approximations of derivatives by finite differences. We give an explicit formula for the bias and derive the convergence rates of the corresponding estimators. Theoretical results are illustrated by numerical examples.

show abstract

“…As already mentioned, most of the existing literature on parameter estimation for SPDEs is focused on sampling the Fourier modes in continuous time. In particular, the MLE approach was successfully applied to nonlinear equations [CGH11,PS19], and to equations driven by a fractional noise [CLP09]. Besides MLEs, in [CGH18] the authors propose an alternative class of estimators, called trajectory fitting estimators, and a Bayesian approach to estimating drift coefficients for a class of SPDEs driven by multiplicative noise is considered in [CCG19].…”

mentioning

confidence: 99%

Drift estimation for discretely sampled SPDEs

Cialenco

Delgado-Vences²,

Kim

2020

Stoch PDE: Anal Comp

View full text Add to dashboard Cite

The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an additive space-time noise. We consider the traditional for stochastic partial differential equations statistical experiment when the measurements are performed in the spectral domain, and in contrast to the existing literature, we study the asymptotic properties of the maximum likelihood (type) estimators (MLE) when both, the number of Fourier modes and the time go to infinity. In the first part of the paper we consider the usual setup of continuous time observations of the Fourier coefficients of the solutions, and show that the MLE is consistent, asymptotically normal and optimal in the mean-square sense. In the second part of the paper we investigate the natural time discretization of the MLE, by assuming that the first N Fourier modes are measured at M time grid points, uniformly spaced over the time interval [0, T ]. We provide a rigorous asymptotic analysis of the proposed estimators when N → ∞ and/or T, M → ∞. We establish sufficient conditions on the growth rates of N, M and T , that guarantee consistency and asymptotic normality of these estimators.

show abstract

Drift estimation for stochastic reaction-diffusion systems

Cited by 18 publications

References 33 publications

Diffusivity Estimation for Activator–Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton

Diffusivity Estimation for Activator–Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton

Statistical analysis of discretely sampled semilinear SPDEs: a power variation approach

Drift estimation for discretely sampled SPDEs

Contact Info

Product

Resources

About