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

Adatom incorporation and step crossing at the edges of 2D nanoislands

Adatom incorporation into the ``faceted'' steps bordering the 2D nanoislands is analyzed. The step permeability and incorporation coefficients are derived for some typical growth situations. It is shown that the step consisting of equivalent straight segments can be permeable even in the case of fast egde migration if there exist factors delaying creation of new kinks. The step consisting of alternating rough and straight segments may be permeable if there is no adatom transport between neighboring segments through the corner diffusion.Comment: 3 pages, one figur

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

Formation of phase structure in the system Ti-3Al at the stage of secondary structurization at synthesis in the mode of thermal explosion

Features of phase formation processes in the system Ti-3Al at realization of self-extending synthesis in the mode of thermal explosion have been established with use of technological reactor enabling instant switching-off of the heating source. The analysis of synthesis finished products allows to draw a conclusion that phase structure of charge is abnormally depends on sizes of titanium particles. The single-phase product corresponding to initial stoichiometry is synthesized on fine and large fractions for the induction period. On intermediate fraction the product of synthesis is multiphas

Formation of phase structure in the system Ti-3Al at the stage of secondary structurization at synthesis in the mode of thermal explosion

Features of phase formation processes in the system Ti-3Al at realization of self-extending synthesis in the mode of thermal explosion have been established with use of technological reactor enabling instant switching-off of the heating source. The analysis of synthesis finished products allows to draw a conclusion that phase structure of charge is abnormally depends on sizes of titanium particles. The single-phase product corresponding to initial stoichiometry is synthesized on fine and large fractions for the induction period. On intermediate fraction the product of synthesis is multiphas

Model-oriented co-design of homogeneous computing systems

This article proposes an approach to the construction of a technological platform for designing function-oriented processors (FOP) built on the basis of homogeneous computing environments (OVS). A feature of the proposed approach is the use of co-design - a simultaneous and interconnected design of hardware (HW) and software (SW) FOP components. The paper presents proposals for the implementation of this approach, based on the use of the prin-ciple of model-based design, which allows you to make the co-design process iterative and effectively distribute data processing procedures between HW and SW - components of FOP. Based on the consideration of the experience in implementing such solutions, the paper presents the composition of functional subsystems of technological platforms, a diagram of information interaction between these subsystems based on intensive using of web-technologies at all stages of the design and operation of FOP. © 2019 Tomsk State University. All rights reserved