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We consider a specific kind of Abstract State Machines. It is shown how the machines can be used to provide a low-level formal semantics for a tiny object-oriented language, including control flow operators , object creation and field manipulation. Then the decidability result is established for checking invariants of programs corresponding to that class of… (More)

This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.

- A Novikov, V Frishling, N Kordzakhia
- 2003

The problem of pricing of time-dependent barrier options is considered in the case when interest rate and volatility are given functions in Black–Scholes framework. The calculation of the fair price reduces to the calculation of non-linear boundary crossing probabilities for a standard Brow-nian motion. The proposed method is based on a piecewise-linear… (More)

The paper reports our ideas and experience on model based testing of a compiler. We consider a tiny programming language that consists of the standard control statements and external method calls only. Static and dynamic semantics of the language is formalized in the Abstract State Machines specification Language (AsmL), and used to produce a test suite for… (More)

Let X 1 , X 2 ,. .. be a discrete-time stochastic process with a distribution P θ , θ ∈ Θ, where Θ is an open subset of the real line. We consider the problem of testing a simple hypothesis H 0 : θ = θ 0 versus a composite alternative H 1 : θ > θ 0 , where θ 0 ∈ Θ is some fixed point. The main goal of this article is to characterize the structure of locally… (More)

- Andrey Novikov
- 2008

Suppose that at any stage of a statistical experiment a control variable X that affects the distribution of the observed data Y can be used. The distribution of Y depends on some unknown parameter θ, and we consider the classical problem of testing a simple hypothesis H 0 : θ = θ 0 against a simple alternative H 1 : θ = θ 1 allowing the data to be… (More)

We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X1, X2,. .. when testing two simple hypotheses about their common density f : f = f0 versus f = f1. As a functional to be minimized, it is used a weighted sum of the average (under f0) sample number and the two types… (More)

The properties of operators with finite memory in terms of their application for measurement-smoothing processing and detection of image brightness-change boundaries are investigated. Examples of forming operators with given properties and examples of their application to processing real images are viewed.

The possibility of using contour analysis was examined for solving the image superimposition problem in multispectral computer vision systems (images that are obtained from the sensors of this system and images that are synthesized on a digital locality map). Unique algorithms and modifications of the known algorithms that allow the solution of the image… (More)

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In… (More)