Alexander Iksanov




Alexander Iksanov

POSITION
Professor, Head of Operations Research Department

WORK EXPERIENCE
1997–2000
Teaching Assistant
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2000–2002
Assistant Professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2002–2009
Associate Professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2004-2006
Deputy dean of Faculty of Cybernetics
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2009-Present
Professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2014–Present
Head of Operations Research Department
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

EDUCATION AND TRAINING


1995
MSc
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2000
PhD
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2008
Doctor of Physics and Mathematics
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

Discrete random combinatorial structures

Research Fields:
Mathematics

Previous and Current Research

Mathematical structures, both deterministic and random, may be divided into two classes: discrete and continuous. In a wide sense, discrete mathematics studies structures with parameters indexed by the elements of discrete sets consisting of "isolated members”. Random discrete structures constitute a broad class of probabilistic objects with the characteristics being random variables indexed by space or time parameters varying discretely. The research of our group aims at a special type of discrete random objects having a so-called “regeneration” property. Generally speaking, regeneration means the invariance of an exchangeable or partially exchangeable random structure, or the family of such structures, under the deletion of a part chosen uniformly at random. This property provides new insights into the relationship between discrete structures and their continuous-time counterparts and proposes new methods of studying their evolution with the help of well-developed techniques fr om the theory of stochastic processes. In particular, our expertise includes:

  • shot noise processes and random processes with immigration;
  • regenerative compositions and partitions;
  • perpetuities;
  • perturbed random walks;
  • functional limit theorems;
  • branching random walks and smoothing transforms;
  • coalescents theory.

Future Projects and Goals

In the near future we intend to continue the aforementioned lines of research as well as start new projects including:

  • analysis of random polynomials and their roots;
  • asymptotic and qualitative analysis of random sieves and stability of point processes;
  • asymptotic analysis of random trees and their profiles using the notion of mod-phi convergence.

Selected Publications

G. Alsmeyer, A. Iksanov, A. Marynych. (2017)
Functional limit theorems for the number of occupied boxes in the Bernoulli sieve,
Stochastic Processes and their Applications, 127, no. 3, 995-1017.

A. Iksanov, Z. Kabluchko, A. Marynych, G. Shevchenko.(2017)
Fractionally integrated inverse stable subordinators,
Stochastic Processes and their Applications, 127, no. 1, 80-106.

A. Iksanov, A. Marynych, M. Meiners. (2017)
Asymptotics of random processes with immigration I: scaling limits,
Bernoulli, 23, no. 2, 1233-1278.

A. Iksanov, A. Marynych, M. Meiners. (2017)
Asymptotics of random processes with immigration II: convergence to stationarity,
Bernoulli, 23, no. 2, 1279-1298.

A. Iksanov (2016)
Renewal theory for perturbed random walks and similar processes.
Birkhäuser: Cham. 

G. Alsmeyer, A. Iksanov, M. Meiners. (2015)
Power and exponential moments of the number of visits and related quantities for perturbed random walks,
Journal of Theoretical Probability, 28, 1-40.

A. Gnedin, A. Iksanov, A. Marynych, M. Moehle. (2014)
On asymptotics of the beta coalescents,
Advances in Applied Probability, 46, no. 2, 496-515.

A. Gnedin, A. Iksanov, A. Marynych. (2014)
Lambda-coalescents: a survey,
Journal of Applied Probability, Special Volume 51A, 23-40.

A. Iksanov, A. Marynych, M. Meiners.(2014)
Limit theorems for renewal shot noise processes with eventually decreasing response functions,
Stochastic Processes and their Applications, 124, no. 6, 2131-2170.

A. Gnedin, A. Iksanov, A. Marynych. (2011)
Lambda-coalescents with dust component,
Journal of Applied Probability, 48, no. 4, 1133-1151.

Contacts

Homepage: http://do.unicyb.kiev.ua/iksan/


iksan@univ.kiev.ua