Related papers: Large deviations for Gaussian diffusions with dela…
Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
The incidence of rare events in fast-slow systems is investigated via analysis of the large deviation principle (LDP) that characterizes the likelihood and pathway of large fluctuations of the slow variables away from their mean behavior --…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the…
An overview of rare events algorithms based on large deviation theory (LDT) is presented. It covers a range of numerical schemes to compute the large deviation minimizer in various setups, and discusses best practices, common pitfalls, and…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive…
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative…