On a unified approach to the analysis of two-sided cumulative sum control schemes with headstarts

1985 ◽  
Vol 17 (03) ◽  
pp. 562-593 ◽  
Author(s):  
Emmanuel Yashchin
Keyword(s):  
Length Distribution ◽  
Sufficient Conditions ◽  
Unified Approach ◽  
Cumulative Sum ◽  
Control Schemes ◽  
The Laplace Transform ◽  
Run Length Distribution ◽  
Cumulative Sum Control ◽  
Necessary And Sufficient ◽  
Control Limits

The necessary and sufficient conditions for various modes of interactions of the upper and lower schemes with headstarts are derived. The expression for the Laplace transform of the run-length distribution (for both interacting and non-interacting schemes) is obtained and used to develop a method of analysis for general two-sided cumulative sum schemes with headstarts. The results are shown to be relevant in the case when the schemes are supplemented by Shewhart’s control limits.

On a unified approach to the analysis of two-sided cumulative sum control schemes with headstarts

1985 ◽  
Vol 17 (3) ◽  
pp. 562-593 ◽  
Author(s):  
Emmanuel Yashchin
Keyword(s):  
Length Distribution ◽  
Sufficient Conditions ◽  
Unified Approach ◽  
Cumulative Sum ◽  
Control Schemes ◽  
The Laplace Transform ◽  
Run Length Distribution ◽  
Cumulative Sum Control ◽  
Necessary And Sufficient ◽  
Control Limits

The necessary and sufficient conditions for various modes of interactions of the upper and lower schemes with headstarts are derived. The expression for the Laplace transform of the run-length distribution (for both interacting and non-interacting schemes) is obtained and used to develop a method of analysis for general two-sided cumulative sum schemes with headstarts. The results are shown to be relevant in the case when the schemes are supplemented by Shewhart’s control limits.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Use of cumulative sum control schemes for monitoring recruitment in clinical trials

1998 ◽  
Vol 19 (3) ◽  
pp. S50
Author(s):  
Stephen F. Bingham ◽  
R. Anne Horney ◽  
Gail F. Kirk ◽  
David G. Weiss ◽  
William O. Williford
Keyword(s):  
Clinical Trials ◽  
Cumulative Sum ◽  
Control Schemes ◽  
Cumulative Sum Control

A Dam with seasonal input

1994 ◽  
Vol 31 (2) ◽  
pp. 526-541 ◽  
Author(s):  
Robert B. Lund
Keyword(s):  
Laplace Transform ◽  
Convergence Rates ◽  
Sufficient Conditions ◽  
Limiting Distribution ◽  
Stochastic Monotonicity ◽  
The Laplace Transform ◽  
Monotonicity Result ◽  
The Mean ◽  
The Moment ◽  
Necessary And Sufficient

This paper examines the infinitely high dam with seasonal (periodic) Lévy input under the unit release rule. We show that a periodic limiting distribution of dam content exists whenever the mean input over a seasonal cycle is less than 1. The Laplace transform of dam content at a finite time and the Laplace transform of the periodic limiting distribution are derived in terms of the probability of an empty dam. Necessary and sufficient conditions for the periodic limiting distribution to have finite moments are given. Convergence rates to the periodic limiting distribution are obtained from the moment results. Our methods of analysis lean heavily on the coupling method and a stochastic monotonicity result.

scholarly journals Analysis of Multiterm Initial Value Problems with Caputo–Fabrizio Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Mohammed Al-Refai ◽  
Muhammed Syam
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Initial Value ◽  
The Laplace Transform ◽  
Necessary And Sufficient

In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the existence of solutions to the problem. We also obtain the solutions in closed forms. We present two examples to illustrate the validity of the obtained results.

scholarly journals Weighted Exponential Inequalities

2001 ◽  
Vol 8 (1) ◽  
pp. 69-86
Author(s):  
H. P. Heinig ◽  
R. Kerman ◽  
M. Krbec
Keyword(s):  
Laplace Transform ◽  
Sufficient Conditions ◽  
Two Dimensions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Inequalities ◽  
Averaging Operator ◽  
The Laplace Transform ◽  
Discrete Analogues ◽  
Carleman’S Inequality ◽  
Necessary And Sufficient

Abstract Necessary and sufficient conditions on weight pairs are found for the validity of a class of weighted exponential inequalities involving certain classical operators. Among the operators considered are the Hardy averaging operator and its variants in one and two dimensions, as well as the Laplace transform. Discrete analogues yield characterizations of weighted forms of Carleman's inequality.

scholarly journals Optimal contracts in continuous-time models

2006 ◽  
Vol 2006 ◽  
pp. 1-27 ◽  
Author(s):  
Jakša Cvitanić ◽  
Xuhu Wan ◽  
Jianfeng Zhang
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Optimal Contract ◽  
Full Information ◽  
Unified Approach ◽  
Optimal Contracts ◽  
Underlying Process ◽  
Portfolio Managers ◽  
The Difference ◽  
Necessary And Sufficient

We present a unified approach to solving contracting problems with full information in models driven by Brownian motion. We apply the stochastic maximum principle to give necessary and sufficient conditions for contracts that implement the so-called first-best solution. The optimal contract is proportional to the difference between the underlying process controlled by the agent and a stochastic, state-contingent benchmark. Our methodology covers a number of frameworks considered in the existing literature. The main finance applications of this theory are optimal compensation of company executives and of portfolio managers.

Macroscopic properties of a linear mosaic

1985 ◽  
Vol 17 (2) ◽  
pp. 330-346 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Length Distribution ◽  
Sufficient Conditions ◽  
General Distribution ◽  
Segment Length ◽  
Complete Coverage ◽  
Limit Theory ◽  
Random Line ◽  
Macroscopic Properties ◽  
Necessary And Sufficient ◽  
Joint Limit

A linear mosaic is a process of random line segments distributed according to a Poisson process. This paper presents a wide-ranging treatment of limit theory for the two major macroscopic properties of a linear mosaic: total vacancy, and total number of spacings (or clumps). These quantities do not admit an explicit, exact treatment, and are perhaps most informatively studied by means of limit theory. We permit segment length to have a general distribution, and study the implications of tail properties of this distribution. Necessary and sufficient conditions are given for vacancy on an interval [0, t] to admit a normal approximation as t →∞. An approximate formula is provided for the probability of complete coverage, in the case of general segment length distribution. In all cases, properties of vacancy and number of spacings are studied together, by means of joint limit theorems, rather than individually, as in some earlier work.

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