
Prof. Dr. Alexander Iksanov,
Operations Research Department,
Faculty of Computer Science and Cybernetics,
Taras Shevchenko National University of Kyiv,
Kyiv01601, Ukraine.
Education and scientific career:
1995  Faculty of Cybernetics, National Taras Shevchenko University of Kyiv
2000  PhD.
2008  Habilitation in Physics and Mathematics (doctor phisykomatematychnyh nauk).
Teaching and other experience:
20022008  associate professor
20042006  deputy dean of faculty of cybernetics
since 2009  professor
since 2014  head of Operations Research Department
20192021 – head of the project no. 19ÁÔ01501 “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 socalled “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 continuoustime counterparts and proposes new methods of studying their evolution with the help of welldeveloped 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 CMJbranching 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 modphi 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, 12331278.
3) A. Iksanov, A. Marynych, M. Meiners.
Asymptotics of random processes with immigration II: convergence to stationarity,
Bernoulli, 23, no. 2, 12791298
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, 9951017.
5) A. Gnedin, A. Iksanov, A. Marynych, M. Moehle. (2018).
The collision spectrum of Lambdacoalescents,
Annals of Applied Probability, 28, no. 6, 38573883.
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, 113.
7) A. Iksanov, B. Mallein. (2019).
A result on power moments of Levytype perpetuities and its application to the L_pconvergence of Biggins' martingales in branching Levy processes,
ALEA  Latin American Journal of Probability and Statistics, 16, 315331.
8) A. Bostan, A. Marynych, K. Raschel. (2019).
On the least common multiple of several random integers,
Journal of Number Theory, 204, 113133.
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, 45854603.
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, 265273.
Contacts
Homepage: http://do.unicyb.kiev.ua/iksan/
Postal address: Taras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, Ukraine, Kyiv03680, Glushkov Av. 4d
Email: iksan@univ.kiev.ua
