A generalized Martingale Theorem

1972 ◽  
Vol 23 (4) ◽  
pp. 289-292 ◽  
Author(s):  
D. Landers ◽  
L. Rogge
Keyword(s):  
Martingale Theorem ◽  
Generalized Martingale

On the weak convergence of U-statistic processes, and of the empirical process

1978 ◽  
Vol 83 (2) ◽  
pp. 269-272 ◽  
Author(s):  
R. M. Loynes
Keyword(s):  
Weak Convergence ◽  
Wiener Process ◽  
Empirical Process ◽  
Convergence Result ◽  
The Other ◽  
Direct Argument ◽  
Random Functions ◽  
Martingale Theorem ◽  
The Relationship ◽  
Special Case

1. Summary and introductionIn (5) a weak convergence result for U-statistics was obtained as a special case of a reverse martingale theorem; in (7) Miller and Sen obtained another such result for U-statistics by a direct argument. As they stand these results are not very closely connected, since one is concerned with U-statistics Uk for k ≥ n, while the other deals with Uk for k ≤ n, but if one instead thinks of k as unrestricted and transforms the random functions Xn which enter into one of these results into new functions Yn by setting Yn(t) = tXn(t−1) one finds that the Yn are (aside from variations in interpolated values) just the functions with which the other result is concerned. As the limiting Wiener process W is well-known to have the property that tW(t−1) is another Wiener process it is not too surprising that both results should hold, and part of the purpose of this paper is to provide a general framework within which the relationship between these results will become clear. A second purpose is to illustrate the simplification that the martingale property brings to weak convergence studies; this is shown both in the U-statistic example and in a new proof of the convergence of the empirical process.

Maximal function on generalized martingale Lebesgue spaces with variable exponent

2013 ◽  
Vol 83 (10) ◽  
pp. 2168-2171 ◽  
Author(s):  
Eiichi Nakai ◽  
Gaku Sadasue
Keyword(s):  
Maximal Function ◽  
Variable Exponent ◽  
Lebesgue Spaces ◽  
Generalized Martingale

scholarly journals Generalized martingale-residual processes for goodness-of-fit inference in Cox's type regression models

1997 ◽  
Vol 25 (2) ◽  
pp. 683-714 ◽  
Author(s):  
Leszek Marzec ◽  
Paweł Marzec
Keyword(s):  
Regression Models ◽  
Goodness Of Fit ◽  
Martingale Residual ◽  
Generalized Martingale

scholarly journals A Generalized Martingale Betting Strategy

2009 ◽  
Vol 21 (3) ◽  
pp. 183-197
Author(s):  
David K. Neal ◽  
Michael D. Russell
Keyword(s):  
Generalized Martingale

Stochastic optimal scheduling of hydropower compensation for wind and photovoltaic power output considering multiple uncertainties

2020 ◽  
Author(s):  
Weifeng Liu ◽  
Chao Wang ◽  
Xiaohui Lei ◽  
Ping-an Zhong ◽  
Qingwen Lu
Keyword(s):  
Stochastic Programming ◽  
Wind Power ◽  
Power Output ◽  
Optimal Scheduling ◽  
Dynamic Update ◽  
Photovoltaic Power ◽  
Stochastic Programming With Recourse ◽  
Multiple Uncertainties ◽  
Generalized Martingale ◽  
Single Power

<p>Multiple uncertainties, including from the uncertainty of a single power (wind power or photovoltaic power) output forecasting to the uncertainty of the combined power output of wind and photovoltaic forecasting to the power shortage after hydropower compensation for wind and photovoltaic power output, exist in the wind-photovoltaic-hydropower system. Furthermore, as the forecast is updated, the above uncertainty will evolve accordingly. Revealing the evolution of multiple uncertainties is of great significance for the hydropower compensation for the combined power output of wind and photovoltaic. We use a generalized martingale model of forecast evolution to describe the uncertainty of a single power output. We then superimpose the single power output to obtain the combined power output of wind and photovoltaic. we establish a stochastic programming with recourse model for optimal scheduling of the hydropower compensation for wind and photovoltaic power output. The results indicate that the uncertainty of the combined power output of wind and photovoltaic forecasting is less than that of wind power output forecasting, and greater than that of photovoltaic power output forecasting. After hydropower compensates for combined power output of wind and photovoltaic, compared with the uncertainty of combined wind and photovoltaic power output forecasting, the uncertainty of power shortage is greatly reduced by 90%, which has significant benefits. And with the dynamic update of the forecast, the uncertainty of the single power output forecast, the uncertainty of the combined power output forecast, and the uncertainty of the power shortage will decrease accordingly.</p>

A LEARNING AUTOMATA-BASED ALGORITHM TO THE STOCHASTIC MIN-DEGREE CONSTRAINED MINIMUM SPANNING TREE PROBLEM

2013 ◽  
Vol 24 (03) ◽  
pp. 329-348 ◽  
Author(s):  
JAVAD AKBARI TORKESTANI
Keyword(s):  
Spanning Tree ◽  
Sampling Method ◽  
Minimum Spanning Tree ◽  
Minimum Weight ◽  
Learning Automata ◽  
Optimal Solution ◽  
Simulation Experiments ◽  
Stochastic Graph ◽  
Standard Sampling ◽  
Martingale Theorem

Min-degree constrained minimum spanning tree (md-MST) problem is an NP-hard combinatorial optimization problem seeking for the minimum weight spanning tree in which the vertices are either of degree one (leaf) or at least degree d ≥ 2. md-MST problem is new to the literature and very few studies have been conducted on this problem in deterministic graph. md-MST problem has several appealing real-world applications. Though in realistic applications the graph conditions and parameters are stochastic and vary with time, to the best of our knowledge no work has been done on solving md-MST problem in stochastic graph. This paper proposes a decentralized learning automata-based algorithm for finding a near optimal solution to the md-MST problem in stochastic graph. In this work, it is assumed that the weight associated with the graph edge is random variable with a priori unknown probability distribution. This assumption makes the md-MST problem incredibly harder to solve. The proposed algorithm exploits an intelligent sampling technique avoiding the unnecessary samples by focusing on the edges of the min-degree spanning tree with the minimum expected weight. On the basis of the Martingale theorem, the convergence of the proposed algorithm to the optimal solution is theoretically proven. Extensive simulation experiments are performed on the stochastic graph instances to show the performance of the proposed algorithm. The obtained results are compared with those of the standard sampling method in terms of the sampling rate and solution optimality. Simulation experiments show that the proposed method outperforms the standard sampling method.

scholarly journals A Note on the ExponentialG-Martingale

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yunsheng Lu ◽  
Yingying Liu
Keyword(s):  
Distinct Difference ◽  
Martingale Theorem

We get the exponentialG-martingale theorem with the Kazamaki condition and tell a distinct difference between the Kazamaki’s and Novikov’s criteria with an example.

scholarly journals The Marcinkiewicz–Zygmund LLN in Banach Spaces: A Generalized Martingale Approach

2009 ◽  
Vol 23 (2) ◽  
pp. 509-522 ◽  
Author(s):  
Florian Hechner ◽  
Bernard Heinkel
Keyword(s):  
Banach Spaces ◽  
Martingale Approach ◽  
Generalized Martingale

Generalized martingale model of the uncertainty evolution of streamflow forecasts

2013 ◽  
Vol 57 ◽  
pp. 41-51 ◽  
Author(s):  
Tongtiegang Zhao ◽  
Jianshi Zhao ◽  
Dawen Yang ◽  
Hao Wang
Keyword(s):  
Streamflow Forecasts ◽  
Generalized Martingale
Sign in / Sign up

Export Citation Format

Share Document