NEWFELPRO's success stories: Nikola Sandrić and Levy process
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Nikola Sandrić, photo taken from the webpage
Nikola Sandrić is one of the first NEWFELPRO fellows in the outgoing scheme who successfully finished with the implementation of his 16 month long project titled Sample Path Properties of Lévy-Type Processes (SPPLTP). Dr. Sandrić conducted his research at the Technical University Dresden (Germany), Institute for Stochastic mathematics, during the outgoing scheme of his project under the mentorship of Dr. René Schilling. He spent his return phase implementing his project at the Faculty of Civil Engineering of the University of Zagreb.
The aim of this project was to study sample path properties of Feller processes associated with pseudo-differential operators, called Lévy-type processes, in terms of the corresponding symbol or, equivalently, Lévy triplet. More precisely, the goal was to study discrete-time (Markov chain) approximations, fluctuations (oscillations), recurrence and transience and certain limiting behaviors (that is, variants of the law of large numbers, law of the iterated logarithm and central limit theorem) of Lévy-type processes on all three levels: bounded coefficients, unbounded coefficients and random coefficients.
Throughout his project he held following presentations of his project and work:
The aim of this project was to study sample path properties of Feller processes associated with pseudo-differential operators, called Lévy-type processes, in terms of the corresponding symbol or, equivalently, Lévy triplet. More precisely, the goal was to study discrete-time (Markov chain) approximations, fluctuations (oscillations), recurrence and transience and certain limiting behaviors (that is, variants of the law of large numbers, law of the iterated logarithm and central limit theorem) of Lévy-type processes on all three levels: bounded coefficients, unbounded coefficients and random coefficients.
Throughout his project he held following presentations of his project and work:
- Long-time behavior of Lévy-type processes: recurrence, transience and ergodicity, Workshop on Stochastic Analysis and Related Topics, Dresden, Germany (2014)
- Ergodicity and fluctuations of a fluid particle driven by diffusions with jumps, Analysis and Stochastics Seminar, Technische Universität Dresden, Dresden, Germany (2014)
- Homogenization of periodic diffusion with small jumps, Probability and Analysis, Bedlewo, Poland (2015)
- Stochastic stability of Markov models, Graduate Lectures in Mathematics, Technische Universität Dresden, Dresden, Germany (2015)
- Ergodicity and fluctuations of a fluid particle driven by a diffusion process with jumps, Summer School on Dirichlet Forms and Stochastic Analysis, Osaka, Japan (2015)
- Long-time behavior of Lévy-type processes: transience, recurrence and ergodicity, German-Japanese Conference on Stochastic Analysis and Applications, Sendai, Japan (2015)
He also participated in a workshop „Dirichlet forms and Stochastic Analysis" (2014) and Erasmus 2015 Summer School for PhD Students in Dresden.
Based on the results of his project, he published following articles:
Pang, Guodong; Sandrić, Nikola. Ergodicity and Fluctuations of a Fluid Particle Driven by Diffusions with Jumps. // Communications in mathematical sciences. 14 (2016) , 2; 327-362
Sandrić, Nikola. Homogenization of periodic diffusion with small jumps. // Journal of mathematical analysis and applications. 435 (2016), 1; 551-577
Sandrić, Nikola. Ergodicity of L\'evy-Type Processes. // ESAIM: Probability and Statistics. (2016) (accepted for publishing in ESAIM-Prob. Stat. 2016)
Sandrić, Nikola. On Transience of L'evy-Type Processes. Stochastics-An International Journal of Probability and Stochastic Processes. (2016) (accepted for publishing in Stocahstics 2016)
Upon finishing his NEWFELPRO project, dr. Sandrić continues with his academic endeavours as an assistant professor at the Faculty of Civil Engineering of the University of Zagreb.
Congratulations!
Congratulations!