scholarly journals Estimates of Certain Exit Probabilities for p-Adic Brownian Bridges

Author(s):  
David Weisbart
2013 ◽  
Vol 50 (1) ◽  
pp. 195-207 ◽  
Author(s):  
Bin Li ◽  
Qihe Tang ◽  
Xiaowen Zhou

We study the two-sided exit problem of a time-homogeneous diffusion process with tax payments of loss-carry-forward type and obtain explicit formulae for the Laplace transforms associated with the two-sided exit problem. The expected present value of tax payments until default, the two-sided exit probabilities, and, hence, the nondefault probability with the default threshold equal to the lower bound are solved as immediate corollaries. A sufficient and necessary condition for the tax identity in ruin theory is discovered.


2016 ◽  
Vol 6 (1) ◽  
pp. 142
Author(s):  
Qiang Zhang ◽  
Michael R. Kosorok

The Brownian bridge is not yet used widely in the statistical monitoring of clinical trials. In this paper, we investigate properties of the Brownian bridge and formally derive monitoring rules from these results. We will present four related main methods: (1). derivation of group sequential boundaries; (2). calculation of conditional power; (3). a new alpha spending function and (4). repeated confidence intervals, all under a Brownian bridge framework. Simulation results show that the type I error rate is well controlled and power is satisfactory for the group sequential design. We apply the proposed methods to monitor the interim results from the Beta Blocker Heart Attack Trial (BHAT) and a Head and Neck cancer trial with comparisons to the commonly used monitoring tools. Overall, the proposed methods when used together as one framework are more powerful and sensitive to interim positive and negative trends that are clinically meaningful and lead to timely early stopping with potentially more savings on sample sizes, time and costs. These tools are valuable additions to the existing group sequential methods which can be utilized in trial design, routine monitoring, and to answer important questions from data monitoring committees.


2007 ◽  
Vol 97 (3) ◽  
pp. 2083-2093 ◽  
Author(s):  
Paul W. German ◽  
Howard L. Fields

Animals return to rewarded locations. An example of this is conditioned place preference (CPP), which is widely used in studies of drug reward. Although CPP is expressed as increased time spent in a previously rewarded location, the behavioral strategy underlying this change is unknown. We continuously monitored rats ( n = 22) in a three-room in-line configuration, before and after morphine conditioning in one end room. Although sequential room visit durations were variable, their probability distribution was exponential, indicating that the processes controlling visit durations can be modeled by instantaneous room exit probabilities. Further analysis of room transitions and computer simulations of probabilistic models revealed that the exploratory bias toward the morphine room is best explained by an increase in the probability of a subset of rapid, direct transitions from the saline- to the morphine-paired room by the central room. This finding sharply delineates and constrains possible neural mechanisms for a class of self-initiated, goal-directed behaviors toward previously rewarded locations.


Sign in / Sign up

Export Citation Format

Share Document