Related papers: Law Of Large Numbers For Random Dynamical Systems
The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter…
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
I explore the possibility that the laws of physics might be laws of inference rather than laws of nature. What sort of dynamics can one derive from well-established rules of inference? Specifically, I ask: Given relevant information…
This paper studies a random differential equation with random switch perturbations. We explore how the maximum displacement from the equilibrium state depends on the statistical properties of time series of {the} random switches. We show a…
The generalized allocation scheme is studied. Its extension for coloured balls is defined. Some analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers are obtained for the number of boxes containing fixed numbers…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of…
The strong law of large numbers for linear combinations of functions of order statistics ($L$-statistics) based on weakly dependent random variables is proven. We also establish the Glivenko--Cantelli theorem for $\phi$-mixing sequences of…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing…
We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
A general method to obtain strong laws of large numbers is studied. The method is based on abstract H\'ajek-R\'enyi type maximal inequalities. The rate of convergence in the law of large numbers is also considered. Some applications for…
In modeling parasitic diseases, it is natural to distinguish hosts according to the number of parasites that they carry, leading to a countably infinite type space. Proving the analogue of the deterministic equations, used in models with…