Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.

Energy amplification in channel flows with stochastic excitation

Abstract: We investigate energy amplification in parallel channel flows, where background noise is modeled as stochastic excitation of the linearized Navier–Stokes equations. We show analytically that the energy of three-dimensional streamwise-constant disturbances achieves O(R3) amplification. Our basic technical tools are explicit analytical calculations of the traces of solutions of operator Lyapunov equations, which yield the covariance operators of the forced random velocity fields. The dependence of these quantities on both the Reynolds number and the spanwise wave number are explicitly computed. We show how the amplification mechanism is due to a coupling between wall-normal velocity and vorticity disturbances, which in turn is due to nonzero mean shear and disturbance spanwise variation. This mechanism is viewed as a consequence of the non-normality of the dynamical operator, and not necessarily due to the existence of near resonances or modes with algebraic growth.

Observable Operator Models for Discrete Stochastic Time Series

Abstract: A widely used class of models for stochastic systems is hidden Markov models. Systems that can be modeled by hidden Markov models are a proper subclass of linearly dependent processes, a class of s...

Detecting Initialization Bias in Simulation Output

Abstract: A general approach to testing for initialization bias in the mean of a simulation output series is presented The output is transformed into a standardized test sequence that can be contrasted with a known limiting stochastic process This transformation requires very little computation and the asymptotic theory is applicable to a wide variety of simulations An initialization bias test is developed and several examples of its application are presented

A Sequential Procedure for Determining the Length of a Steady-State Simulation

Abstract: A common problem faced by simulators is that of constructing a confidence interval for the steady-state mean of a stochastic process. We have reviewed the existing procedures for this problem and found that all but one either produce confidence intervals with coverages which may be considerably lower than desired or have not been adequately tested. Thus, in many cases simulators will have more confidence in their results than is justified. In this paper we present a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level. The procedure has the advantage that it does not explicitly require a stochastic process to have regeneration points. Empirical results for a large number of stochastic systems indicate that the new procedure performs quite well.