Related papers: Mapping multiplicative to additive noise
A simple sparse coding mechanism appears in the sensory systems of several organisms: to a coarse approximation, an input $x \in \R^d$ is mapped to much higher dimension $m \gg d$ by a random linear transformation, and is then sparsified by…
We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…
We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry--Esseen bound of the so-called alternative estimator of the mean reversion parameter. The…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before…
A stochastic process that arises by composing a function with a Markov process is called an aggregated Markov process (AMP). The purpose of composing a Markov process with a function can be a reduction of dimensions, e.g., a projection onto…
Stochastic Bloch equations which model the fluorescence of two level molecules and atoms, NMR experiments and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is…
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…
In the context of track fitting problems by a Kalman filter, the appropriate functional forms of the elements of the random process noise matrix are derived for tracking through thick layers of dense materials and magnetic field. This work…
Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
The study of diffusion and low frequency vibrational motions of particles on metal surfaces is of paramount importance; it provides valuable information on the nature of the adsorbate-substrate and the substrate-substrate interactions. In…
We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein…
We consider a stochastic process with long-range dependence perturbed by multiplicative noise. The marginal distributions of both the original process and the noise have regularly-varying tails, with tail indices $\alpha,\alpha'>0$,…
This work is devoted to deriving the Onsager--Machlup function for a class of degenerate stochastic dynamical systems with (non-Gaussian) L\'{e}vy noise as well as Brownian noise. This is obtained based on the Girsanov transformation and…
This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…
We have generalized the semi-analytic approach of special flow to the description of flows of passive particles taking into account internal noise. The model is represented by a series of recurrence relations. The recurrence relations are…
Recent experiments have shown that stochastic effects exerted at the level of translation contribute a substantial portion of the variation in abundance of proteins expressed at moderate to high levels. This study analyzes translational…