Related papers: Filtering theory for a weakly coloured noise proce…
The optical light curves of many quasars show variations of tenths of a magnitude or more on time scales of months to years. This variation often cannot be described well by a simple deterministic model. We perform a Bayesian comparison of…
The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would…
This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…
Rough stochastic differential equations (RSDEs) are common generalisations of Ito SDEs and Lyons RDEs and have emerged as new tool in several areas of applied probability, including non-linear stochastic filtering, pathwise stochastic…
The objective in stochastic filtering is to reconstruct information about an unobserved (random) process, called the signal process, given the current available observations of a certain noisy transformation of that process. Usually X and Y…
We propose a novel time-splitting scheme for a class of semilinear stochastic evolution equations driven by cylindrical fractional noise. The nonlinearity is decomposed as the sum of a one-sided, non-globally, Lipschitz continuous function,…
In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The Linear Inverse Model (LIM) is a class of data-driven methods that extract dynamic and stochastic…
In this paper we introduce a new approach to the study of filtering theory by allowing the system's parameters to have a random character. We use Hida's white noise space theory to give an alternative characterization and a proper…
We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fokker-Planck equation. First, we prove a superposition…
State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…
We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…
We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with…
A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck noise $\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\eta$ is described by a Markov process in two dimensions. But even though there exists a…
An efficient despeckling method using a quantum-inspired adaptive threshold function is presented for reducing noise of ultrasound images. In the first step, the ultrasound image is decorrelated by an spectrum equalization procedure due to…
We consider multiscale stochastic dynamical systems. In this article an \emph{intermediate} reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially…
The study of thermodynamic properties of microscopic systems, such as a colloid in a fluid, has been of great interest to researchers since the discovery of the fluctuation theorem and associated laws of stochastic thermodynamics. However,…
We study stochastic model reduction for evolution equations in infinite dimensional Hilbert spaces, and show the convergence to the reduced equations via abstract results of Wong-Zakai type for stochastic equations driven by a scaled…
The small noise cut-off phenomenon in continuous time and space has been studied in the recent literature for the linear and non-linear stable Langevin dynamics with additive L\'evy drivers - understood as abrupt thermalization of the…
The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as…
In this paper we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or…