Date:
Speaker: Yuliya Mishura, Taras Shevchenko National University of Kyiv
Time : 15:00 - 16.00 CET (Rome/Paris)
Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Zoom : A zoom meeitng link will appear here, one hour before the talk
Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
* SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus
Keywords: fractional integral; fractional derivative; fractional Gaussian process
Abstract: We start with the simplest case of Riemann-Liouville fractional operators to demonstrate how they generate fractional Brownian motion. This is the example of Gaussian-Volterra process with the kernel created by power functions, see [1]. Now two ways are possible: to generalize the kernel itself and obtain the new processes ([2]) or to consider more general fractional operators and also generate Gaussian processes ([3,4]). We shall realize both ways and consider some properties of the respective processes.
Biography: Yuliya Mishura received her PhD in probability and statistics in Kyiv University in 1978 and completed her postdoctoral degree in probability and statistics (Habilitation) in 1990. She is currently a Professor of the Department of Probability, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. Having broad and varied scientific interests, she is the author/coauthor of more than 320 research papers and more than 20 books. Her research interests include theory and statistics of stochastic processes, stochastic differential equations, fractional calculus and fractional processes, stochastic analysis, functional limit theorems, entropies of probability distributions and stochastic systems, financial mathematics and other applications of stochastics. Invited speaker of many international congresses and conferences, organizer of series of conferences. Editor-in-chief of the journal “Theory of Probability and Mathematical Statistics”, coeditor-in-chief of the journal “Modern Stochastics: Theory and Applications”. Team leader and participant of many international research projects.
Bibliography
[1] Yuliya Mishura “Stochastic calculus for fractional Brownian motion and related processes”. Springer Berlin Heidelberg (2008)
[2] Yuliya Mishura, Georgij Shevchenko, Sergej Shklyar. “Gaussian processes with Volterra kernels”. In: International Conference on Stochastic Processes and Algebraic Structures Cham: Springer International Publishing (2019), pp. 249-276
[3] Luisa Beghin, Lorenzo Cristofaro, Yuliya Mishura. “A class of processes defined in the white noise space through generalized fractional operators”. In: Stochastic Processes and their Applications, 178, 104494 (2024).
[4] Luisa Beghin, Alessandro De Gregorio, A., Yuliya Mishura. (2025). “Hadamard fractional Brownian motion: path properties and Wiener integration”. In: arXiv preprint arXiv:2507.13512 (2025)
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