L2 Stochastic Processes

Ash, Robert B.; Gardner, Melvin F.

doi:10.1016/b978-0-12-065270-9.50004-4

Cited by 109 publications

(149 citation statements)

References 0 publications

Supporting

Mentioning

145

Contrasting

Unclassified

Order By: Relevance

“…Note that Z 0 ∼ µ and Z t is a stationary process. It is easy to see that Y t and Z t have the same distribution since we can identify R 2 with C [2,19]. Hence, by (8) we have…”

mentioning

confidence: 87%

The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields

Chen

Xiong

et al. 2016

Journal of Mathematical Physics

View full text Add to dashboard Cite

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steadystate fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes have not been rigorously proved yet due to technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function.The proof is based on the Karhunen-Loéve expansion of complex-valued 1 LDP of entropy production rate in magnetic fields 2 Ornstein-Uhlenbeck process.

show abstract

“…Note that Z 0 ∼ µ and Z t is a stationary process. It is easy to see that Y t and Z t have the same distribution since we can identify R 2 with C [2,19]. Hence, by (8) we have…”

mentioning

confidence: 87%

The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields

Chen

Xiong

et al. 2016

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…First we note the following simple statement about the existence of L 2 -limits (see, e.g., Ash and Gardner [4], Theorem 1.3.2).…”

Section: -Riemann Integral Of a Process Along A Curvementioning

confidence: 99%

Estimation of the Mean of a Wiener Sheet

Baran

Pap

Zuijlen

2004

Statistical Inference for Stochastic Processes

View full text Add to dashboard Cite

A standard Wiener sheet shifted by an unknown parameter is observed above a decreasing curve Γ. By the help of a direct discrete approach and under weaker assumptions than in the paper of Arató, N. M. [3], an explicit formula is derived for the maximum likelihood estimator (MLE) of the shift parameter. The MLE is a weighted linear combination of the values at the endpoints of the curve Γ and weighted integrals of the observed process and its normal derivative along the curve Γ.Keywords. Wiener sheet, Radon-Nikodym derivatives, maximum likelihood estimator, stochastic integral along a curve, weighted integral of the normal derivative of a random process along a curve.

show abstract

“…., are the functional principal components (FPCs) of the random trajectories X i which are uncorrelated random variables with E(ξ ik ) = 0, Ash and Gardner 1975). The eigenfunctions φ k are the solutions of the eigen-equations G(s, t)φ k (s) ds = λ k φ k (t), k = 1, 2, .…”

Section: Functional Principal Componentsmentioning

confidence: 99%

A stickiness coefficient for longitudinal data

Gottlieb

Müller

2012

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

In this paper, we introduce the stickiness coefficient, a summary statistic for time-course and longitudinal data, which is designed to characterize the time dynamics of such data. The stickiness coefficient provides a simple, intuitive and informative measure that captures key information contained in time-course data. Under the assumption that the data are generated by the trajectories of a smooth underlying stochastic process, the stickiness coefficient illuminates the relationship between the value of the process at one time with the value it assumes at another time via a single numeric measure. In particular, the stickiness coefficient summarizes the extent to which deviations from the mean trajectory tend to co-vary over time. The estimation scheme we propose will allow for estimation even in the case that the longitudinal data are sparsely observed at irregular times and may be corrupted by noise. We demonstrate an estimation procedure for the stickiness coefficient and establish asymptotic consistency as well as asymptotic convergence rates. We illustrate the resulting stickiness coefficient with some theoretical calculations as well as several economic and health related data examples.

show abstract

L2 Stochastic Processes

Cited by 109 publications

References 0 publications

The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields

The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields

Estimation of the Mean of a Wiener Sheet

A stickiness coefficient for longitudinal data

Contact Info

Product

Resources

About