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Gorshenin A.K.,Russian Academy of Sciences | Korolev V.Y.,Russian Academy of Sciences | Zeifman A.I.,Vologda State Pedagogical University | Shorgin S.Y.,Russian Academy of Sciences | And 3 more authors.
AIP Conference Proceedings | Year: 2013

A micro-scale model is proposed for the evolution of such information system as the limit order book in financial markets. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of buy and sell orders that determine the price discovery mechanism. The proposed multiplicative model of stochastic intensities makes it possible to analyze the characteristics of the order flows as well as the instantaneous proportion of the forces of buyers and sellers, that is, the imbalance process, without modelling the external information background. The proposed model gives the opportunity to link the micro-scale (high-frequency) dynamics of the limit order book with the macro-scale models of stock price processes of the form of subordinated Wiener processes by means of limit theorems of probability theory and hence, to use the normal variance-mean mixture models of the corresponding heavy-tailed distributions. The approach can be useful in different areas with similar properties (e.g., in plasma physics). © 2013 AIP Publishing LLC.


Zeifman A.,Vologda State Pedagogical University | Korotysheva A.,Vologda State Pedagogical University | Shorgin S.,Vologda State Pedagogical University | Bening V.,Moscow State University
VALUETOOLS 2011 - 5th International ICST Conference on Performance Evaluation Methodologies and Tools | Year: 2011

We study Mt/Mt /N/N+R queue and obtain stability bounds for main characteristics of the respective queue-length process. Copyright © 2011 ICST.


Kalinicheva O.V.,Vologda State Pedagogical University | Tomanov V.P.,Vologda State Pedagogical University
Kinematics and Physics of Celestial Bodies | Year: 2012

We consider the connection with Uranus for: (1) 945 near-parabolic comets (the period P > 200 years, the perihelion distance q > 0.1 AU), (2) 1277 Kreutz comets (P > 200 years, q < 0.01 AU), and (3) 414 short-period comets (P < 200 years). It turns out that none of near-parabolic comets passed through Uranus's activity sphere, none of the Kreutz comets approach Uranus closer than 11 AU, and only two short-period comets, C/2006 U7 and C/2006 F2, could have a close approach to Uranus during 5000 years. © 2012 Allerton Press, Inc.


Zeifman A.,Vologda State Pedagogical University | Korotysheva A.,Vologda State Pedagogical University | Satin Y.,Vologda State Pedagogical University
2010 International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, ICUMT 2010 | Year: 2010

We obtain some stability bounds for nonstationary Erlang loss queueing model. Two specific examples of queues with close to periodic arrival and service rates are considered. ©2010 IEEE.


Zeifman A.,Vologda State Pedagogical University | Korotysheva A.,Vologda State Pedagogical University | Satin Y.,Vologda State Pedagogical University | Shilova G.,Vologda State Pedagogical University | Panfilova T.,Vologda State Pedagogical University
Communications in Computer and Information Science | Year: 2013

An analogue of Mt /Mt/S/S Erlang loss system for a queue with group services is introduced and considered. Weak ergodicity of the model is studied. We obtain the bounds on the rate of convergence to the limiting characteristics and consider two concrete queueing models with finding of their main limiting characteristics. © 2013 Springer-Verlag.


Kalinicheva O.V.,Vologda State Pedagogical University | Tomanov V.P.,Vologda State Pedagogical University
Kinematics and Physics of Celestial Bodies | Year: 2010

The hypothesis on the genetic connection of near-parabolic comets with Jupiter, Saturn, and the transPlutonian region (5-3000 AU) proposed by E. M. Drobyshevskii is considered. It has been shown that, on average, 5.6 comets per an area of 106 AU2 passed through the transPlutonian region during the whole history of observations. Six-hundred nineteen comets crossed the ecliptic at heliocentric distances ranging from 0 to 2 AU. As has been shown, from the total number of 945 near-parabolic comets, eight comets closely approached Jupiter and five closely approached Saturn. The Kreutz comets, 1277 objects, did not approach Jupiter closer than 3 AU. Their minimal distance to Saturn was 5.5 AU. The minimal distance of the Kreutz comets from the edge of the transPlutonian region was 28.8 AU. The analysis led to the conclusion that the concept on the origin of the near-parabolic comets suggested by Drobyshevskii is groundless. © 2010 Allerton Press, Inc.


Zeifman A.,Vologda State Pedagogical University | Satin Y.,Vologda State Pedagogical University | Panfilova T.,Vologda State Pedagogical University
Mathematical Biosciences | Year: 2013

General nonstationary birth-death process with possible catastrophes on finite state space is studied. The approach for obtaining the bounds on the rates of convergence to the limiting characteristics is outlined. Method for construction of the limiting characteristics is proposed. We also show that, as a rule, the initial conditions quickly become irrelevant. An example of respective process is shown in details. © 2013 Elsevier Inc.


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PubMed | Vologda State Pedagogical University
Type: Journal Article | Journal: Mathematical biosciences | Year: 2013

General nonstationary birth-death process with possible catastrophes on finite state space is studied. The approach for obtaining the bounds on the rates of convergence to the limiting characteristics is outlined. Method for construction of the limiting characteristics is proposed. We also show that, as a rule, the initial conditions quickly become irrelevant. An example of respective process is shown in details.

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