Vadym Radchenko




Vadym Radchenko

POSITION
Professor of Department of Mathematical Analysis

WORK EXPERIENCE
1989-1990
Research scientists
Zaporizhzhya State University, Zaporizhzhya, (Ukraine)

1990-1991
Assistant professor
Zaporizhzhya State University, Zaporizhzhya, (Ukraine)

1991-1992
Lecturer
Zaporizhzhya State University, Zaporizhzhya, (Ukraine)

1992-1994
Associate Professor
Zaporizhzhya State University, Zaporizhzhya, (Ukraine)

1994-1997
Doctorant
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine).

1997-2008
Associate Professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

2008–Present
Professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

EDUCATION AND TRAINING

1985
BSc + MSc
Taras Shevchenko National University of Kiev, Kyiv (Ukraine)

1989
Ph.D
Taras Shevchenko National University of Kiev, Kyiv (Ukraine)

2008
DSc (Habilitation)
Taras Shevchenko National University of Kiev, Kyiv (Ukraine)

Stochastic measures, stochastic integration, stochastic partial differential equations, regularity properties of random processes

Research Fields:
Mathematics

Previous and Current Research

  • Integration with respect to stochastic measures
  • Path properties of stochastic measures
  • Stochastic partial differential equations driven by stochastic measures
  • Stochastic equations driven by stochastic measures in Hilbert spaces
  • Integration of random functions with respect to deterministic measures
  • Financial mathematics

Our research deals with stochastic measures (L0-valued vector measures) as stochastic integrator. Martingals, fractional Brownian motion, stable measures are the partial cases of stochastic measures.

Path properties of related processes were studied. For some equations driven by stochastic measures existence and uniqueness of solutions, regularity properties of the solutions were investigated.

Now we study new classes of partial differential equation driven by stochastic measures, equations in infinite-dimensional spaces, asymptotic behavior of the solutions.

We maintain collaboration with Friedrich-Schiller University of Jena (Germany).

Future Projects and Goals

  • Asymptotic behavior of the solutions of equations driven by stochastic measures
  • Approximate methods for equations driven by stochastic measures
  • Properties of equations with symmetric integral of random function with respect to stochastic measures
  • Stochastic equations driven by stochastic measures in infinite-dimensional spaces

Selected Publications

Radchenko V.
Stratonovich-type integral with respect to a general stochastic measure.

Stochastics. – 2016. – Vol. 88 (7). – P. 1060-1072.

Radchenko V.
Evolution equations with general stochastic measures in Hilbert space.
Theory of Probability and Its Applications. – 2015. – Vol. 59 (2). – P. 328-339.

Radchenko V.
Stochastic partial differential equations driven by general stochastic measures.
In: Modern Stochastics and Appl. (V.Korolyuk, N.Limnios, Yu.Mishura, L.Sakhno, G.Shevchenko, Eds.), Springer, 2014. – P. 143-156.

Radchenko V.
Riemann integral of a random function and the parabolic equation with a general stochastic measure.
Theory of Probability and Mathematical Statistics. – 2013. – Vol. 87. – P. 185-198.

Radchenko V., Zähle M.
Heat equation with a general stochastic measure on nested fractals.
Statistics and Probability Letters. – 2012. – Vol. 82 (3). – P. 699-704.

Radchenko V.
Paths of stochastic measures and Besov spaces.
Theory of Probability and Its Applications. – 2010. – Vol. 59 (1). – P. 160-168.

Radchenko V.
Mild solution of the heat equation with a general stochastic measure.
Studia Mathematica. – 2009. – Vol. 194 (3). – P. 231-251.

Radchenko V.
Variance-minimizing hedging in a model with jumps at Poisson random times.
Theory of Probability and Mathematical Statistics. – 2009. – Vol. 78. – P. 175-190.

Radchenko V.
Heat equation and wave equation with general stochastic measures.
Ukrainian Mathematical Journal. –2008. – Vol. 60 (12).– P. 1968—1981.

Radchenko V.
Besov regularity of stochastic measures.
Statistics and Probability Letters. – 2007. – Vol. 77 (8). – P. 822-825.

Radchenko V.
Variance-minimizing hedging in a model with jumps at deterministic times.
Theory of Probability and Its Applications. – 2007. – Vol. 51 (3). – P. 536-545.

Contacts

Homepage: http://www.mechmat.univ.kiev.ua/eng/ppages/radchenko


vradchenko@univ.kiev.ua