Related papers: Stochastic monotonicity from an Eulerian viewpoint
We introduce a novel type of random perturbation for the classical Lorenz flow in order to better model phenomena slowly varying in time such as anthropogenic forcing in climatology and prove stochastic stability for the unperturbed flow.…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
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 define the empiric stochastic stability of an invariant measure in the finite-time scenario, the classical definition of stochastic stability. We prove that an invariant measure of a continuous system is empirically stochastically stable…
A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian)…
We consider random walk among iid, uniformly elliptic conductances on $\mathbb Z^d$, and prove the Einstein relation (see Theorem 1). It says that the derivative of the velocity of a biased walk as a function of the bias equals the…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
We consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
Given two random variables $X$ and $Y$, stochastic monotonicity describes a monotone influence of $X$ on $Y$. We prove two different characterizations of stochastically monotone $2$-copulas using the isomorphism between $2$-copulas and…