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 (L_{0}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 infinitedimensional spaces, asymptotic behavior of the solutions.
We maintain collaboration with FriedrichSchiller 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 infinitedimensional spaces
Selected Publications
Radchenko V.
Stratonovichtype integral with respect to a general stochastic measure.
Stochastics. – 2016. Vol. 88 (7). P. 10601072.
Radchenko V.
Evolution equations with general stochastic measures in Hilbert space.
Theory of Probability and Its Applications. 2015. Vol. 59 (2). P. 328339.
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. 143156.
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. 185198.
Radchenko V., Zähle M.
Heat equation with a general stochastic measure on nested fractals.
Statistics and Probability Letters. 2012. Vol. 82 (3). P. 699704.
Radchenko V.
Paths of stochastic measures and Besov spaces.
Theory of Probability and Its Applications. 2010. Vol. 59 (1). P. 160168.
Radchenko V.
Mild solution of the heat equation with a general stochastic measure.
Studia Mathematica. 2009. Vol. 194 (3). P. 231251.
Radchenko V.
Varianceminimizing hedging in a model with jumps at Poisson random times.
Theory of Probability and Mathematical Statistics. 2009. Vol. 78. P. 175190.
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. 822825.
Radchenko V.
Varianceminimizing hedging in a model with jumps at deterministic times.
Theory of Probability and Its Applications. 2007. Vol. 51 (3). P. 536545.
Contacts
Homepage: http://www.mechmat.univ.kiev.ua/eng/ppages/radchenko
vradchenko@univ.kiev.ua
