Most Efficient Homogeneous Volatility Estimators

We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We introduce the "quasi-unbiased estimators", that can address any type of desirable constraints. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval in the form of the joint distributions of the high-minus-open, low-minus-open and close-minus-open values, whose analytical expression is derived exactly for Wiener processes with drift. The distributions can be calculated to yield the most efficient estimators associated with any statistical properties of the underlying log-price stochastic process. Applied to Wiener processes for log-prices with drift, we provide explicit analytical expressions for the most efficient point-wise volatility and variance estimators, based on the analytical expression of the joint distribution of the high-minus-open, low-minus-open and close-minus-open values. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass, Roger-Satchell and maximum likelihood estimators.Comment: 46 pages including 17 figure

Spurious trend switching phenomena in financial markets

The observations of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years reported by Preis et al. (2010, 2011), are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection of price peaks that imposes a condition on the statistics of price change and of trade volumes that skew their distributions. For the intertrade times, the extrema and power laws results from the format of transaction dat

Bridge homogeneous volatility estimators

We present a theory of bridge homogeneous volatility estimators for log-price stochastic processes. Starting with the standard definition of a Brownian bridge as the conditional Wiener process with two endpoints fixed, we introduce the concept of an incomplete bridge by breaking the symmetry between the two endpoints. For any given time interval, this allows us to encode the information contained in the open, high, low and close prices into an incomplete bridge. The efficiency of the new proposed estimators is favourably compared with that of the classical Garman–Klass and Parkinson estimators

Simulation of non-stationary processes in industrial centrifugal cascades of uranium enrichment

The mathematical model of non-stationary dividing processes of uranium enrichment in industrial centrifugal cascades which can be used in a computer simulator to prepare experts in dividing production and application as an expert system in the automated control system of technological circuit has been developed and realized

Цифровая фотосъемка произведений живописи

Работа посвящена обзору публикаций в области цифровой фотосъемки произведений искусства. Анализ опубликованных работ показал, что данная тема недостаточно освещена в отечественной литературе — отсутствует общепринятая методика оценки качества цифровых копий произведений живописи. В работе систематизированы требования к технологии получения цифровых копий, такие как порядок съемки и фотографические приемы, представлена оригинальная методика фотографирования.The work presents a review of publications in the field of digital photography works of art. This subject is poorly lit — is absent common method of evaluation of the quality digital copies works of art. Requirements for the technology of digital copies, such as shooting sequence and photographic receptions were systematized in the article. The original technique of photographing presented