Related papers: On the stability of matrix-valued Riccati diffusio…
Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy…
The stability of a recently developed piecewise flat Ricci flow is investigated, using a linear stability analysis and numerical simulations, and a class of piecewise flat approximations of smooth manifolds is adapted to avoid an inherent…
Our current understanding of fluctuations of dynamical (time-integrated) observables in non- Markovian processes is still very limited. A major obstacle is the lack of an appropriate theoretical framework to evaluate the associated large…
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…
Studying the stability of the Kalman filter whose measurements are randomly lost has been an active research topic for over a decade. In this paper we extend the existing results to a far more general setting in which the measurement…
A stable approach for integrating the impedance matrix in cylindrical, radial inhomogeneous structures is developed and studied. A Stroh-like system using the time-harmonic displacement-traction state vector is used to derive the Riccati…
Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch,…
This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…
In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…
This article is concerned with the well-posedness of the "filtering equations", due to Zakai and Kushner-Stratonovich, arising in nonlinear stochastic filtering. In general situations, notably in correlated diffusion models and when signal…
A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features…
We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer…
Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but…
We study the response of the quasi-energy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic…
This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…
The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic…