Related papers: Using Ornstein-Uhlenbeck Process to understand Den…
Active Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models include also random noise in particle displacement (Wiener process) resulting in a…
This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by…
We use Brownian dynamics simulations to study a model of a cyclic bacterial heat engine based on a harmonically confined colloidal probe particle in a bath formed by active Brownian particles. For intermediate activities, active noise…
In this thesis, we consider an $N$-dimensional Ornstein-Uhlenbeck (OU) process satisfying the linear stochastic differential equation $d\mathbf x(t) = - \mathbf B\mathbf x(t) dt + \boldsymbol \Sigma d \mathbf w(t).$ Here, $\mathbf B$ is a…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
Identifying the full entropy production of active particles is a challenging task. We introduce a microscopic, thermodynamically consistent model, which leads to active Ornstein-Uhlenbeck statistics in the continuum limit. Our minimal model…
This paper is concerned with the numerical integration of stochastic differential equations (SDEs) which govern diffusion processes driven by a standard Wiener process. With the latter being replaced by a sequence of increments at discrete…
We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…
We study the non-Markovian random continuous processes described by the Mori-Zwanzig equation. As a starting point, we use the Markovian Gaussian Ornstein-Uhlenbeck process and introduce an integral memory term depending on the past of the…
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
The purpose of this article is a set-indexed extension of the well-known Ornstein-Uhlenbeck process. The first part is devoted to a stationary definition of the random field and ends up with the proof of a complete characterization by its…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
Consider a periodic, mean-reverting Ornstein-Uhlenbeck process $X=\{X_t,t\geq0\}$ of the form $d X_{t}=\left(L(t)+\alpha X_{t}\right) d t+ dB^H_{t}, \quad t \geq 0$, where $L(t)=\sum_{i=1}^{p}\mu_i\phi_i (t)$ is a periodic parametric…
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…
We study the chaotic motion of a semi-classical optomechanical system coupled to a non-Markovian environment with a finite correlation time. We show that the non-Markovian environment can significantly enhance chaos, by studying the…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
Diffusion Probabilistic Models (DPMs) have achieved great success in image generation but suffer from high inference latency due to their iterative denoising nature. Motivated by the evolving feature dynamics across the denoising…
Methods for out-of-distribution (OOD) detection that scale to 3D data are crucial components of any real-world clinical deep learning system. Classic denoising diffusion probabilistic models (DDPMs) have been recently proposed as a robust…
We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…