Related papers: Stochastic Stability
Consequences of quantum recurrences on the stability of a broad class of dynamical systems is presented.
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
We briefly review the topic of AdS (in)stability, mainly focusing on a recently introduced analytic approach and its interplay with numerical results.
We present a new method to analytically prove global stability in ghost-ridden dynamical systems. Our proposal encompasses all prior results and consequentially extends them. In particular, we show that stability can follow from a conserved…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
In this article, we study the persistence of properties of a given classical deter-ministic dierential equation under a stochastic perturbation of two distinct forms: external and internal. The rst case corresponds to add a noise term to a…
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 general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of…
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…
The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just…
This paper considers the problem of finite-time stability for stochastic nonlinear systems. A new Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing…
In reinforcement learning episodes, the rewards and punishments are often non-deterministic, and there are invariably stochastic elements governing the underlying situation. Such stochastic elements are often numerous and cannot be known in…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…