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We study parametric estimation for second order linear parabolic stochastic partial differential equations (SPDEs) in two space dimensions driven by two types of $Q$-Wiener processes based on high frequency spatio-temporal data. First, we…

Statistics Theory · Mathematics 2025-04-15 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

We study parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions with a small dispersion parameter using high frequency data with respect to time and space. We set two…

Statistics Theory · Mathematics 2022-06-22 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

We deal with parameter estimation for a linear parabolic second-order stochastic partial differential equation in two space dimensions driven by two types of $Q$-Wiener processes based on high frequency data with respect to time and space.…

Statistics Theory · Mathematics 2023-04-20 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned…

Statistics Theory · Mathematics 2020-08-13 Yusuke Kaino , Masayuki Uchida

We consider parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a $Q$-Wiener process with a small noise based on high frequency spatio-temporal data. We…

Statistics Theory · Mathematics 2024-08-06 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

We study parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a $Q$-Wiener process based on high frequency spatio-temporal data. We give an estimator of…

Statistics Theory · Mathematics 2024-07-02 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

We consider parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) from high frequency data which are observed in time and space. By using thinned data obtained from the high frequency…

Statistics Theory · Mathematics 2019-10-01 Yusuke Kaino , Masayuki Uchida

We consider parameter estimation of the reaction term for a second order linear parabolic stochastic partial differential equation in two space dimensions driven by a $Q$-Wiener process under small diffusivity. We first construct an…

Statistics Theory · Mathematics 2024-04-04 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…

Statistics Theory · Mathematics 2024-07-26 Randolf Altmeyer , Anton Tiepner , Martin Wahl

The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space.…

Statistics Theory · Mathematics 2021-03-30 Randolf Altmeyer , Markus Reiß

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…

Statistics Theory · Mathematics 2019-11-26 Florian Hildebrandt , Mathias Trabs

This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…

We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency…

Statistics Theory · Mathematics 2025-04-23 Markus Bibinger , Patrick Bossert

We analyse a second-order SPDE model in multiple space dimensions and develop estimators for the parameters of this model based on discrete observations of a solution in time and space on a bounded domain. While parameter estimation for one…

Statistics Theory · Mathematics 2023-11-17 Patrick Bossert

We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of…

Statistics Theory · Mathematics 2019-09-11 Markus Bibinger , Mathias Trabs

We consider a problem of parameter estimation for the state space model described by linear stochastic differential equations. We assume that an unobservable Ornstein-Uhlenbeck process drives another observable process by the linear…

Statistics Theory · Mathematics 2022-03-25 Masahiro Kurisaki

We consider the Cauchy problem for a linear stochastic partial differential equation. By extending the parametrix method for PDEs whose coefficients are only measurable with respect to the time variable, we prove existence, regularity in…

Probability · Mathematics 2019-12-13 Andrea Pascucci , Antonello Pesce

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

Numerical Analysis · Mathematics 2020-01-27 Antoine Tambue , Jean Daniel Mukam

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…

Statistics Theory · Mathematics 2021-08-17 Randolf Altmeyer , Till Bretschneider , Josef Janák , Markus Reiß

This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form of mild solutions in an abstract Hilbert space framework suitable for…

Numerical Analysis · Mathematics 2023-01-16 Giulia Di Nunno , Salvador Ortiz-Latorre , Andreas Petersson
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