Alexander Iksanov




Alexander Iksanov

Prof. Dr. Alexander Iksanov,
Operations Research Department,
Faculty of Computer Science and Cybernetics,
Taras Shevchenko National  University of Kyiv,
Kyiv-01601, Ukraine.

 

Education and scientific career:
1995 - Faculty of Cybernetics, National Taras Shevchenko University of Kyiv
2000 - PhD.
2008 - Habilitation in Physics and Mathematics (doctor phisyko-matematychnyh nauk).

Teaching and other experience:
2002-2008 - associate professor
2004-2006 - deputy dean of faculty of cybernetics
since 2009 - professor
since 2014 - head of Operations Research Department

2019-2021 – head of the project no. 19ÁÔ015-01 “Asymptotic and structural analysis of stochastic models of population dynamics”

Scientific interests in 2019:
1. Random discrete structures (random compositions, coalescents, branching processes etc.).
2. Functional limit theorems.
3. Random processes with immigration (these are renewal shot noise processes with random response functions).
4. Applications of the renewal theory.

Probability, Stochastic Processes

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 from the theory of stochastic processes. 

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;

  • investigation of CMJ-branching processes with random characteristics; 

  • 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;

  • asymptotic analysis of complex systems.

Methodological and Technical Expertise

In particular, our expertise includes:

  • shot noise processes and random processes with immigration;

  • regenerative compositions and partitions;

  • perpetuities and perturbed random walks;

  • functional limit theorems;

  • branching processes; in particular, branching random walks with real and complex parameters, and smoothing transforms;

  • theory of coalescents;

  • asymptotic properties of stochastic evolution equations.

Selected Publications

1) A. Iksanov (2016)

Renewal theory for perturbed random walks and similar processes. 

Probability and its Applications, Birkhäuser.


2) A. Iksanov, A. Marynych, M. Meiners. (2017) 

Asymptotics of random processes with  immigration I: scaling limits,

Bernoulli, 23, no. 2, 1233-1278.


3) A. Iksanov, A. Marynych, M. Meiners. 

Asymptotics of random processes with  immigration II: convergence to stationarity

Bernoulli, 23, no. 2, 1279-1298 


4) 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.


5) A. Gnedin, A. Iksanov, A. Marynych, M. Moehle. (2018).

The collision spectrum of Lambda-coalescents,

Annals of Applied Probability, 28, no. 6, 3857-3883.


6) A. Iksanov, Z. Kabluchko. (2018).

A functional limit theorem for the profile of random recursive trees,

Electronic Communications in Probability, 23, paper no. 87, 1-13.


7) A. Iksanov, B. Mallein. (2019).

A result on power moments of Levy-type perpetuities and its application to the L_p-convergence of Biggins' martingales in branching Levy processes,

ALEA - Latin American Journal of Probability and Statistics, 16, 315-331.


8) A. Bostan, A. Marynych, K. Raschel. (2019).

On the least common multiple of several random integers,

Journal of Number Theory, 204, 113-133.


9) G. Alsmeyer, Z. Kabluchko, A. Marynych. (2019).

Limit theorems for the least common multiple of a random set of integers,

Transactions of the American Mathematical Society, 372, no. 7, 4585-4603.


10) I. V. Samoilenko,  A. V. Nikitin. (2019)

Double merging of the phase space for stochastic differential equations with small additions in Poisson approximation conditions.

Cybernetics and System Analysis, 55, no. 2, 265-273.



Contacts

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

Postal address: Taras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, Ukraine, Kyiv-03680, Glushkov Av. 4d

Email: iksan@univ.kiev.ua