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Journals and Conferences
Experimental results of investigation of two-photon interactions at LEP (CERN) are presented. Experimental conditions provided a possibility of investigation of the whole set of two-photon interactions from the production of lepton pairs in collisions of quasi-real photons to interactions of high-virtual photons. PACS numbers: 13.40.-f, 13.66.De DOI:… (More)
Scan statistics are commonly used in biology, medicine, engineering and other fields where interest is in the probability of observing clusters of events in a window at an unknown location. Due to the dependent nature of the number of events in a large number of overlapping window locations, even approximate solutions for the simplest scan statistics may… (More)
Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the… (More)
In this paper we introduce a <i>randomly</i> truncated sequential hypothesis test. Using the framework of a repeated significance test (RST), we study a sequential test with truncation time based on a random stopping time. Using the functional central limit theorem (FCLT) for a sequence of statistics, we derive a general result that can be employed in… (More)
A new martingale technique is developed to find formulas for the first two moments and generating function of the waiting time until one observes an element of a finite collection of patterns in a finite multi-state Markov chain.
Methods using gambling teams and martingales are developed and applied to find formulas for the expected value and the generating function of the waiting time until observes one of the elements of a finite collection of patterns in a sequence which is generated by a two-state Markov chain. (Keywords: Gambling, teams, waiting times, patterns, success runs,… (More)
We show how martingale techniques (both old and new) can be used to obtain otherwise hard-to-get information for the moments and distributions of waiting times for patterns in independent or Markov sequences. In particular, we show how these methods provide moments and distribution approximations for certain scan statistics, including about variable length… (More)
The expected value and generating function of the number of overlapping occurrences of a pattern P in a Markov chain until the first occurrence of a member from a finite collection of patterns that start with P is obtained. A martingale technique is employed to address the problem.
We survey the ways that martingales and the method of gambling teams can be used to obtain otherwise hard-to-get information for the moments and distributions of waiting times for the occurrence of simple or compound patterns in an independent or a Markov sequence. We also survey how such methods can be used to provide moments and distribution… (More)