Related papers: Stochastic Reservoir Calculations
From the observation of a diffusion path $(X_t)_{t\in [0,T]}$ on a compact connected $d$-dimensional manifold $\mathcal{M}$ without boundary, we consider the problem of estimating the stationary measure $\mu$ of the process. Wang and Zhu…
A minimal model for reservoir computing is studied. We demonstrate that a reservoir computer exists that emulates given coupled maps by constructing a modularized network. We describe a possible mechanism for collapses of the emulation in…
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…
A natural hypothesis for the success of reservoir computing in generic tasks is the ability of the untrained reservoir to map different input time series to separable reservoir states - a property we term separation capacity. We provide a…
Reservoir computing is a well-established approach for processing data with a much lower complexity compared to traditional neural networks. Despite two decades of experimental progress, the core properties of reservoir computing (namely…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
Let $(X,\p_x)$ be a continuous time Markov chain with finite or countable state space $S$ and let $T$ be its first passage time in a subset $D$ of $S$. It is well known that if $\mu$ is a quasi-stationary distribution relatively to $T$,…
We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of…
In this paper, we analyze a discrete-time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The stationary distribution of the customer count…
From a high volume stream of weighted items, we want to maintain a generic sample of a certain limited size $k$ that we can later use to estimate the total weight of arbitrary subsets. This is the classic context of on-line reservoir…
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems…
We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We…
We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed…
Within the framework of stochastic inflationary cosmology we derive steady-state distributions P_c(V) of domains in comoving coordinates, under the assumption of slow-rolling and for two specific choices of the coarse-grained inflaton…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
Stochastic precipitation generators (SPGs) are a class of statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate…
The infinite (in both directions) sequence of the distributions $\mu^{(k)}$ of the stochastic integrals $\int_0^{\infty-}c^{-N_{t-}^{(k)}} dL_t^{(k)}$ for integers $k$ is investigated. Here $c>1$ and $(N_t^{(k)},L_t^{(k)})$, $t\geq0$, is a…
We show that Zhang's sandpile model (N,[a,b]) on N sites and with uniform additions on [a,b] has a unique stationary measure for all 0 <= a < b <= 1. This generalizes earlier results where this was shown in some special cases. We define the…
One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…