Related papers: Large deviations for Gaussian diffusions with dela…
We study a stochastic multiscale spatial gene network. These naturally arise in molecular biology. In our model, the reactants are subject to on-site reactions on both scales and diffusion on the continuous scale only, although diffusion on…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel,…
We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…
In this paper, we present the discrete-time unbiased extremum seeking (ES) algorithm for n-dimensional (nD) static quadratic maps in the presence of unknown time-varying measurement delays bounded by known constants which can be large. The…
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of…
Tracer diffusion in single-file systems, where particles are restricted to move on a line without passing each other, has been a fertile ground to investigate anomalous diffusion and strong memory effects. While the long-time behavior of…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
Gaussian macroscopic fluctuation theory underpins the understanding of noise in a broad class of nonequilibrium systems. We derive exact fluctuation-response relations linking the power spectral density of stationary fluctuations to the…
Dynamic gene-regulatory networks are complex since the number of potential components involved in the system is very large. Estimating dynamic networks is an important task because they compromise valuable information about interactions…
We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
Diffusion models achieve state-of-the-art generation quality across many applications, but their ability to capture rare or extreme events in heavy-tailed distributions remains unclear. In this work, we show that traditional diffusion and…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…
We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The…
Are there hidden dynamical common patterns in the evolution of social and cultural history? While the growing availability of digitized social data invites us to answer this question, prevailing quantitative methods often rely on…
Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the…