The Value of Knowing that You Do Not Know

The value of knowing about data availability and system accessibility is analyzed through theoretical models of Information Economics. When a user places an inquiry for information, it is important for the user to learn whether the system is not accessible or the data is not available, rather than not have any response. In reality, various outcomes can be provided by the system: nothing will be displayed to the user (e.g., a traffic light that does not operate, a browser that keeps browsing, a telephone that does not answer); a random noise will be displayed (e.g., a traffic light that displays random signals, a browser that provides disorderly results, an automatic voice message that does not clarify the situation); a special signal indicating that the system is not operating (e.g., a blinking amber indicating that the traffic light is down, a browser responding that the site is unavailable, a voice message regretting to tell that the service is not available). This article develops a model to assess the value of the information for the user in such situations by employing the information structure model prevailing in Information Economics. Examples related to data accessibility in centralized and in distributed systems are provided for illustration.

Hyper-random Phenomena: Definition and Description

The paper is dedicated to the theory which describes physical phenomena in non-constant statistical conditions. The theory is a new direction in probability theory and mathematical statistics that gives new possibilities for presentation of physical world by hyper-random models. These models take into consideration the changing of object’s properties, as well as uncertainty of statistical conditions.

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.

Branching Stochastic Processes: History, Theory, Applications

Косто В. Митов - Разклоняващите се стохастични процеси са модели на популационната динамика на обекти, които имат случайно време на живот и произвеждат потомци в съответствие с дадени вероятностни закони. Типични примери са ядрените реакции, клетъчната пролиферация, биологичното размножаване, някои химични реакции, икономически и финансови явления. В този обзор сме се опитали да представим съвсем накратко някои от най-важните моменти и факти от историята, теорията и приложенията на разклоняващите се процеси.

Probabilistic Models in Cryptography, Coding Theory and Tests for PRNG

2000 Mathematics Subject Classification: 94A29, 94B70

On Special Case of Multiple Hypotheses Optimal Testing for Three Differently Distributed Random Variables

2000 Mathematics Subject Classification: 62P30.