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We study a simple model of the stochastic information filtering, in a randomly organized information system. For simplest versions of the model it appears to be possible to describe the filtering dynamics in terms of the master equations.…
The archetypal system demonstrating stochastic resonance is nothing more than a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a…
It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…
This article investigates stochastic epidemic models with partial information and addresses the estimation of current values of not directly observable states. The latter is also called nowcasting and related to the so-called "dark figure"…
We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative noise arising from a control parameter of the system. Contrary to the…
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…
We deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. Previous works by several authors have shown that the error structure of the method is characterized by…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
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…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [14]. We use the model to simulate two different types…
We study a class of filters -- discrete finite-state transition systems employed as incremental stream transducers -- that have application to robotics: e.g., to model combinatorial estimators and also as concise encodings of feedback…
We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…
We consider a setting, where the output of a linear dynamical system (LDS) is, with an unknown but fixed probability, replaced by noise. There, we present a robust method for the prediction of the outputs of the LDS and identification of…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…