The continuum Kardar-Parisi-Zhang equation in one dimension is lattice discretized in such a way that the drift part is divergence free. This allows to determine explicitly the stationary measures. We map the lattice KPZ equation to a bosonic field theory which has a cubic anti-hermitian nonlinearity. Thereby it is established that the stationary two-point function spreads superdiffusively.

This paper is concerned with solving single CVaR and mixed CVaR minimization problems. A CHKS-type smoothing sample average approximation (SAA) method is proposed for solving these two problems, which retains the convexity and smoothness of the original problem and is easy to implement. For any fixed smoothing constant 2, this method produces a sequence whose cluster points are weak stationary ...

We consider some classes of stationary, counting{measure{valued Markov processes and their companions under time{reversal. Examples arise in the L evy{It^ o decomposition of stable Ornstein{Uhlenbeck processes, the large{time asymptotics of the standard additive coalescent, and extreme value theory. These processes share the common feature that points in the support of the evolving counting{ me...

To a given finite graph we associate three kinds of adic, or BratteliVershik, systems: stationary, symbol-count, and reinforced. We give conditions for the natural walk measure to be adic-invariant and identify the ergodic adicinvariant measures for some classes of examples. If the walk measure is adicinvariant we relate its ergodic decomposition to the vector of limiting edge traversal frequen...

We present data-dependent learning bounds for the general scenario of nonstationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. We use our learning bounds to devise new algorithms for non-stationary time series forecastin...

Abstract A connection between the response and fluctuation in general nonequilibrium stationary states is investigated. We focus on time-symmetric quantities find that of a kind empirical measure can be expressed with measure, current, current. This relation proven by using fictitious stalling decomposition: we decompose single observed transition (edge state space) two microscopic into transit...

The author proposes stochastic approximation methods of finding the optimal measure change by the exponential tilting for Lévy processes in Monte Carlo importance sampling variance reduction. In accordance with the structure of the underlying Lévy measure, either a constrained or unconstrained algorithm of the stochastic approximation is chosen. For both cases, the almost sure convergence to a ...

The problem of predicting a sequence x1, x2, .... where each xi belongs to a finite alphabet A is considered. Each letter xt+1 is predicted using information on the word x1, x2, ...., xt only. We use the game theoretical interpretation which can be traced to Laplace where there exists a gambler who tries to estimate probabilities for the letter xt+1 in order to maximize his capital . The optima...

We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical s...

In this paper, we develop mathematical machinery for verifying that a broad class of general state space Markov chains reacts smoothly to certain types of perturbations in the underlying transition structure. Our main result provides conditions under which the stationary probability measure of an ergodic Harris recurrent Markov chain is diierentiable in a certain strong sense. The approach is b...