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Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…

Segmented models are widely used to describe non-stationary sequential data with discrete change points. Their estimation usually requires solving a mixed discrete-continuous optimization problem, where the segmentation is the discrete part…

For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally…

This paper proposes a hierarchical modeling approach to perform stochastic model specification in Markov switching vector error correction models. We assume that a common distribution gives rise to the regime-specific regression…

We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…

This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…

We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial…

We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…

Some elements of the theory and algorithmics corresponding to the computation of semilinear sparse models for discrete-time signals are presented. In this study, we will focus on approximately eventually periodic discrete-time signals, that…

This book is an introduction to the theory of stochastic partial differential equations (SPDEs), using the random field approach pioneered by J.B. Walsh (1986). It consists of two blocks: the core matter (Chapters 1 to 6) and the appendices…

We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly non-linear, Stefan-type condition. We show that proper separation of phases is attained, i.e., the solution…

We study a class of stochastic time-fractional equations on $\mathbb{R}^d$ driven by a centered Gaussian noise, involving a Caputo time derivative of order $\beta>0$, a fractional (power) Laplacian of order $\alpha>0$, and a…

The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…

The numerical analysis of stochastic parabolic partial differential equations of the form $$ du + A(u) = f \,dt + g \, dW, $$ is surveyed, where $A$ is a partial operator and $W$ a Brownian motion. This manuscript unifies much of the theory…

In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…