Related papers: Linear State space theory in the white noise space…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
We present a comprehensive study of the phase transitions in the single-field reaction-diffusion stochastic systems with field-dependent mobility of a power-low form and the internal fluctuations. Using variational principles and mean-field…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
We introduce a stochastic partial differential equation capable of reproducing the main features of spatiotemporal intermittency (STI). Additionally the model displays a noise induced transition from laminarity to the STI regime. We show by…
State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…
We develop a quantum field theory based on random nonHermitian actions, which upon quantization lead to stochastic nonlinear Schr\"{o}dinger dynamics for the state vector. In this framework, Lorentz and spacetime translation symmetries are…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more…
Utilization of noise for the control of a class of non-linear systems is presented. The application of state-multiplicative noise as a mean of control is far more limited then the use of standard determinis?tic gains. Nevertheless, so…
In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and…
This paper investigates the influence of environmental noise on the characteristic timescale of the dynamics of density-dependent populations. General results are obtained on the statistics of time spent in rarity and time spent in…
Covariant stochastic partial differential equations are studied in any dimension. A special class of such equations is selected and it is proven that the solutions can be analytically continued to Minkowski space-time yielding tempered…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic…