Integral functionals under the excursion measure

2020 ◽  
Vol 57 (1) ◽  
pp. 137-155
Author(s):  
Maciej Wiśniewolski
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Stochastic Analysis ◽  
New Method ◽  
Theoretic Approach ◽  
Integral Functionals ◽  
New Approach ◽  
Brownian Motion With Drift ◽  
Classical Potential ◽  
Excursion Measure

AbstractA new approach to the problem of finding the distribution of integral functionals under the excursion measure is presented. It is based on the technique of excursion straddling a time, stochastic analysis, and calculus on local time, and it is done for Brownian motion with drift reflecting at 0, and under some additional assumptions for some class of Itó diffusions. The new method is an alternative to the classical potential-theoretic approach and gives new specific formulas for distributions under the excursion measure.

scholarly journals A BSDE APPROACH TO THE SKOROKHOD EMBEDDING PROBLEM FOR THE BROWNIAN MOTION WITH DRIFT

2008 ◽  
Vol 08 (01) ◽  
pp. 35-46 ◽  
Author(s):  
STEFAN ANKIRCHNER ◽  
GREGOR HEYNE ◽  
PETER IMKELLER
Keyword(s):  
Brownian Motion ◽  
Stopping Time ◽  
Embedding Problem ◽  
New Approach ◽  
Martingale Representation ◽  
Classical Version ◽  
Brownian Motion With Drift ◽  
First Moment ◽  
Representation Techniques ◽  
Skorokhod Embedding Problem

We solve Skorokhod's embedding problem for Brownian motion with linear drift (Wt + κ t)t≥0 by means of techniques of stochastic control theory. The search for a stopping time T such that the law of WT + κ T coincides with a prescribed law μ possessing the first moment is based on solutions of backward stochastic differential equations of quadratic type. This new approach generalizes an approach by Bass [3] of the classical version of Skorokhod's embedding problem using martingale representation techniques.

A New Approach for the Analysis of Mixture Toxicity Data

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2345-2348 ◽  
Author(s):  
C. N. Haas
Keyword(s):  
Quantitative Analysis ◽  
Mixture Toxicity ◽  
New Method ◽  
Metal Exposure ◽  
Positive Interactions ◽  
Toxicity Data ◽  
Data Set ◽  
New Approach ◽  
Negative Interactions

A new method for the quantitative analysis of multiple toxicity data is described and illustrated using a data set on metal exposure to copepods. Positive interactions are observed for Ni-Pb and Pb-Cr, with weak negative interactions observed for Ni-Cr.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

Self-avoiding random walk: A Brownian motion model with local time drift

1987 ◽  
Vol 74 (2) ◽  
pp. 271-287 ◽  
Author(s):  
J. R. Norris ◽  
L. C. G. Rogers ◽  
David Williams
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Motion Model ◽  
Time Drift ◽  
Brownian Motion Model

Comparison of New Telescopic Video Microlaryngoscopic and Standard Microlaryngoscopic Techniques

1992 ◽  
Vol 101 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Eiji Yanagisawa ◽  
Ken Yanagisawa ◽  
Jay B. Horowitz ◽  
Lawrence J. Mambrino
Keyword(s):  
Video Camera ◽  
New Method ◽  
Depth Of Field ◽  
Microscopic Technique ◽  
New Approach ◽  
Advantages And Disadvantages ◽  
Laryngeal Surgery ◽  
Valuable Method ◽  
Microlaryngeal Surgery ◽  
Television Image

A new approach to microlaryngeal surgery using a specially designed video microlaryngoscope with a rigid endoscopic telescope and an attached video camera was introduced by Kantor et al in 1990. The ability to video document and perform surgery of the larynx by viewing a high-resolution television image was demonstrated. This method was recommended over the standard microscopic technique for increased visibility with greater depth of field, unimpeded instrument access, instant documentation, and superior teaching value. The authors tried this new method and the standard microscopic technique at the same sitting on a series of patients. This paper will compare these two different techniques and discuss their advantages and disadvantages. Although the new method has many advantages, the standard microscopic technique remains as a valuable method in laryngeal surgery.

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