Related papers: Stochastic integral and series representations for…
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…
Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
Stochastic representation for interaction of quantum systems is formulated which allows to replace some of them by equivalent but purely commutative random sources. The formalism is applied to two-level systems interacting with Gaussian…
We present two linear relations between an arbitrary (real tempered second order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic process can…
We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
Stationary (limiting) distributions of shot noise processes, with exponential response functions, form a large subclass of positive selfdecomposable distributions that we illustrate by many examples. These shot noise distributions are…
Stochastic branching algorithms provide a useful alternative to grid-based schemes for the numerical solution of partial differential equations, particularly in high-dimensional settings. However, they require a strict control of the…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
An earlier paper presented the potentially significant discovery that disturbances in simplified simulations of a stellar disc model that was predicted to be stable in linear theory grew to large amplitude over a long period of time. The…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…