The aim of this work is to give an overview of the recent developments in the area of
statistical inference for parabolic stochastic partial differential equations. Significant part of …

There are textbooks and there are research monographs. Some believe that a research
monograph is supposed to bore rather than batter. The following quotation is attributed to …

We consider a parameter estimation problem of determining the viscosity ν of a
stochastically perturbed 2D Navier–Stokes system. We derive several different classes of …

A theory for diffusivity estimation for spatially extended activator–inhibitor dynamics
modeling the evolution of intracellular signaling networks is developed in the mathematical …

A parameter estimation problem is considered for a stochastic parabolic equation driven by
additive Gaussian noise that is white in time and space. The estimator is of spectral type and …

For the stochastic heat equation with multiplicative noise we consider the problem of
estimating the diffusivity parameter in front of the Laplace operator. Based on local …

In this paper we consider the Cauchy problem for second-order stochastic partial differential
equations of parabolic type. We study linear and nonlinear equations for filtering Markov …

We derive consistent and asymptotically normal estimators for the drift and volatility
parameters of the stochastic heat equation driven by an additive space-only white noise …

We analyze the least squares estimator for the drift parameter of an infinite-dimensional
fractional Ornstein–Uhlenbeck process with Hurst parameter H⩾ 1 2. This estimator can be …

We study parameter estimation problem for diagonalizable stochastic partial differential
equations driven by a multiplicative fractional noise with any Hurst parameter H∈(0, 1). Two …