Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017

482 Pages·2018·9.08 MB·English

by  Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić

Springer Proceedings in Mathematics & Statistics
Sergei Silvestrov
Anatoliy Malyarenko
Milica Rančić    Editors
Stochastic
Processes and
Applications
SPAS2017, Västerås and Stockholm,
Sweden, October 4–6, 2017
Springer Proceedings in Mathematics & Statistics
Volume 271
Springer Proceedings in Mathematics & Statistics
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Sergei Silvestrov Anatoliy Malyarenko
(cid:129)
č ć
Milica Ran i
Editors
Stochastic Processes
and Applications
ä å
SPAS2017, V ster s and Stockholm, Sweden,
–
October 4 6, 2017
123
Editors
SergeiSilvestrov Milica Rančić
Division of AppliedMathematics, School Division of AppliedMathematics, School
ofEducation,CultureandCommunication ofEducation,CultureandCommunication
Mälardalen University Mälardalen University
Västerås,Sweden Västerås,Sweden
Anatoliy Malyarenko
Division of AppliedMathematics, School
ofEducation,CultureandCommunication
Mälardalen University
Västerås,Sweden
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-030-02824-4 ISBN978-3-030-02825-1 (eBook)
https://doi.org/10.1007/978-3-030-02825-1
LibraryofCongressControlNumber:2018958926
MathematicsSubjectClassification(2010): 00A69,60-XX
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Dedicated to
Professor Dmitrii S. Silvestrov’s
70th birthday
Preface
Thisbookhighlightsthelatestadvancesinstochasticprocesses,probabilitytheory,
mathematical statistics, engineering mathematics and applications of algebraic
structures, with a focus on those mathematical models, structures, concepts, prob-
lemsandcomputationalmethodsandalgorithmsthatareimportantforapplications
inmoderntechnology,engineeringandthenaturalsciences.Inparticular,thebook
features mathematical methods and models from probability theory, stochastic
processes, applied algebraic structures and computational modelling with various
applications.
The book gathers selected, high-quality contributed chapters from several large
researchcommunitiesworkingonmodernstochasticprocesses,algebraicstructures
and their interplay and applications. The chapters cover both theory and applica-
tions, and are illustrated with a wealth offigures, schemes, algorithms, tables and
findings to help readers grasp the material, and to encourage them to develop new
mathematical methods and concepts in their future research. Presenting new
methods and results, reviews of cutting-edge research, and open problems and
directions for future research, they will serve as a source of inspiration for a broad
range of researchers and research students in, e.g. probability theory and mathe-
matical statistics, applied algebraic structures, and applied mathematics.
This work arose on the basis of contributions presented at the International
Conference “Stochastic Processes and Algebraic Structures — From Theory
Towards Applications” (SPAS2017), which was held in honour of Professor
Dmitrii Silvestrov’s 70th birthday and his 50 years of fruitful service to mathe-
matics, education and international cooperation. This international conference
brought together a selected group of mathematicians, researchers from related
subjects and practitioners from industry who actively contribute to the theory and
applications of stochastic processes and algebraic structures, methods and models.
It was co-organised by the Division of Applied Mathematics, Mälardalen
University, Västerås and the Department of Mathematics, Stockholm University,
Stockholm and held in Västerås and Stockholm, Sweden on 4–6 October 2017.
vii
viii Preface
Representingthefirstoftwovolumes,thebookconsistsof19chapters(papers),
startingwithaspecialchapterdevotedtobiographicalnotesaboutProfessorDmitrii
SilvestrovandwrittenbySergeiSilvestrov,OlaHössjer,AnatoliyMalyarenkoand
Yuliya Mishura. The remaining 18 chapters are grouped into Part I — Stochastic
Processes, and Part II — Applications of Stochastic Processes.
Part I begins with Chap. 2 by Dmitrii Silvestrov, which presents a survey of
research results obtained by him and his colleagues in the areas of limit theorems
for Markov-type processes and randomly stopped stochastic processes, renewal
theory and ergodic theorems for perturbed stochastic processes, quasi-stationary
distributionsforperturbedstochasticsystems,methodsofstochasticapproximation
for price processes, asymptotic expansions for nonlinearly perturbed semi-Markov
processes, and applications of the above results to queuing systems, reliability
models, stochastic networks, bio-stochastic systems, perturbed risk processes and
American-type options.
Chapter 3 by Dmitrii Silvestrov presents results of the complete analysis and
classification of individual ergodic theorems for perturbed alternating regenerative
processes with semi-Markov modulation. New short, long and super-long time
ergodic theorems for regularly and singularly perturbed alternating regenerative
processes are provided.
Chapter 4 by Sergey Krasnitskiy and Oleksandr Kurchenko explores asymp-
totics for Baxter-type sums for generalised random Gaussian fields. The general
results are illustrated on examples related to generalised fields with independent
values and the field offractional Brownian motion.
InChap.5bySalwaBajja,KhalifaEs-SebaiyandLauriViitasaari,upperbounds
for rates of convergence in limit theorems for quadratic variations of the
Lei–Nualart process are presented.
Chapter6byYuliyaMishura,KostiantynRalchenkoandSergiyShklyarfocuses
on parameter estimation in the regression Gaussian model with discrete and con-
tinuous time observations. General results are applied to a number of models such
as fractional Brownian motion, mixed fractional Brownian motion and
sub-fractionalBrownianmotion,aswellasamodelwithtwoindependentfractional
Brownian motions.
In Chap. 7 by Gulnoza Rakhimova, new effective conditions of asymptotic
consistencyforfixed-widthconfidenceintervalestimatorsandasymptoticefficiency
of stopping times are highlighted.
InChap.8byJoséIgorMorlanesandAndriyAndreev,aneffectivealgorithmfor
the simulation of fractional Ornstein–Uhlenbeck process of the second kind is
developed.
Chapter 9 by Kristoffer Lindensjö focuses on an extension of the constructive
martingalerepresentationtheorem,fromthespaceofsquare integrablemartingales
to the space of local martingales.
In Chap. 10 by Anatoliy Malyarenko and Martin Ostoja-Starzewski, random
fields related to the symmetry classes of second-order symmetric tensors are
described.
Preface ix
Part II begins with Chap. 11 by Dmitrii Silvestrov, Mikael Petersson and Ola
Hössjer, in which asymptotic expansions for stationary and conditional
quasi-stationary distributions of nonlinearly perturbed birth–death-type semi-
Markov models are presented, and their applications to models of population
growth, epidemic spread of disease and dynamics of the genetic composition of a
given population are discussed.
Chapter 12 by Ola Hössjer, Günter Bechly and Ann Gauger addresses waiting
times for coordinated mutations in a population described by Markov process of
Morantype.Theauthorsconductadetailedanalysisofthecorrespondingformsand
conditions for waiting time asymptotics.
Chapter 13 by Kristoffer Spricer and Pieter Trapman presents the results of
experimental studies of the initial phase of epidemic growth in large mostly sus-
ceptiblepopulations.Theauthorsdemonstratethattheempiricalnetworkstestedin
theirpaperdisplayexponentialgrowthintheearlystagesoftheepidemic,exceptin
cases where the networks are restricted by strong low-dimensional spatial
constraints.
Chapter 14 by Elena Boguslavskaya, Yuliya Mishura and Georgiy Shevchenko
studiesWiener-transformablemarkets,wherethedrivingprocessisprovidedbyan
adapted transformation of a Wiener process. The authors also investigate the
conditions of replication contingent claims on such markets.
Chapter 15 by Guglielmo D’Amico, Fulvio Gismondi and Filippo Petroni
investigatesthehighfrequencydynamicoffinancialvolumesoftradedstocksusing
asemi-Markovmodel.Theauthorsshowthatthismodelcansuccessfullyreproduce
several empirical facts about volume evolution like time series dependence,
intra-daily periodicity and volume asymmetry.
In Chap. 16 by Benard Abola, Pitos Seleka Biganda, Christopher Engström,
John Magero Mango, Godwin Kakuba and Sergei Silvestrov, new recurrent algo-
rithms with linear time complexity for computing PageRanks for information net-
works with different graph structures are described.
In Chap. 17 by Pitos Seleka Biganda, Benard Abola, Christopher Engström,
JohnMageroMango,GodwinKakubaandSergeiSilvestrov,traditionalPageRanks
based on an ordinary random walk approach and Lazy PageRanks based on a lazy
random walk ona graph interpretationare considered. Further,thepaper describes
how the two variants change when complete graphs are connected to a line of
nodes, the links of which are all in one direction. Explicit formulas and numerical
results are obtained for both PageRank variants.
Chapter 18 by Hannes Malmberg and Ola Hössjer examines continuous
approximations of discrete choice models with a large number of options. The
authors use point process theory and extreme value theory to derive analytic
expressionsforthecontinuousapproximationsunderawiderangeofdistributional
assumptions.
Chapter19byBorisFaybishenko,FredMolzandDeborahAgarwalpresentsthe
results of sensitivity analysis for nonlinear dynamics simulation of ecological
processes based on models of deterministic chaos and their comprehensive time
series analysis in the time domain and phase space.
x Preface
This book was made possible by the strategic support offered by Mälardalen
University to the research environment Mathematics and Applied Mathematics
(MAM) in the established research specialisation of Educational Sciences and
MathematicsattheSchoolofEducation,CultureandCommunicationatMälardalen
University. We are grateful to both the Department of Mathematics, Stockholm
UniversityandtotheMathematicsandAppliedMathematicsresearchenvironment
MAM, Division of Applied Mathematics, School of Education, Culture and
Communication at Mälardalen University, Västerås for their valued support and
cooperation in jointly organising the successful international conference
SPAS2017, which led to this book. We also wish to extend our thanks to the
Swedish International Development Cooperation Agency (Sida) and International
Science Programme in Mathematical Sciences (ISP), the Nordic Council of
MinistersNordplusProgramme,andmanyothernationalandinternationalfunding
organisations, as well as the research and education environments and institutions
of the individual researchers and research teams who were instrumental to the
success of SPAS2017 and to this book. In closing, we wish to especially thank all
of the authors for their excellent contributions to this book. We also wish to thank
thestaffofthepublisher,Springer,fortheiroutstandingsupportwiththisbook.All
of the chapters have been reviewed, and we are grateful to the reviewers for their
diligence.
Västerås, Sweden Sergei Silvestrov
July 2018 Anatoliy Malyarenko
Milica Rančić