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The stochastic duel with time-dependent hit probabilities

✍ Scribed by C. J. Ancker Jr.

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
354 KB
Volume
31
Category
Article
ISSN
0894-069X

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✦ Synopsis

Abstract

The fundamental stochastic duel considers two opponents who fire at each other at either random continuous or fixed‐time intervals with a constant hit probability on each round fired. Each starts with an unloaded weapon, unlimited ammunition, and unlimited time. The first to hit wins. In this article we extend the theory to the case where hit probabilities are functions of the time since the duel began. First, the marksman firing at a passive target is considered and the characteristic function of the time to a hit is developed. Then, the probability of a given side winning the duel is derived. General solutions for a wide class of hit probability functions are derived. Specific examples of both the marksman and the duel problem are given.

πŸ“œ SIMILAR VOLUMES

Stochastic duels with multiple hits and
Stochastic duels with multiple hits and limited ammunition supply
✍ Tai Young Kwon; Do Sun Bai πŸ“‚ Article πŸ“… 1983 πŸ› John Wiley and Sons 🌐 English βš– 418 KB

## Abstract Ancker's stochastic duels with limited ammunition supply are extended to cases where a kill is obtained through repetitive multiple hits with two firing modes, single‐shot firing and pattern firing. Examples with negative exponential firing time and geometric ammunition supply are given

The distribution of the time-duration of
The distribution of the time-duration of stochastic duels
✍ C. J. Ancker Jr.; A. V. Gafarian πŸ“‚ Article πŸ“… 1965 πŸ› John Wiley and Sons 🌐 English βš– 607 KB

The Theory of Stochastic Duels i s extended by considering the d i stribution of time -to-completion of the fundamental duel. The model has fixed kill probabilities and either random o r fixed t i m e between rounds fired. Time-limitation i s included. Special c a s e s and examples a r e worked out

On the stochastic theory of compartments
On the stochastic theory of compartments: Solution for n-compartment systems with irreversible, time-dependent transition probabilities
✍ M. Cardenas; J.H. Matis πŸ“‚ Article πŸ“… 1974 πŸ› Springer 🌐 English βš– 584 KB

The bivariate distribution of a two-compartment stochastic system with irreversible, time-dependent transition probabilities is obtained for any point in time. The mean and variance of the number of particles in any compartment and the covariance between the number of particles in each of the two co