Who I am
I am presently a post-doc working in collaboration with professor Leonid Mytnik at the Israel Institute of Technology - Technion. My present research project investigates the (multi)fractal geometry of continuous random trees and measure-valued processes such as Lévy super-Brownian motion. I am happily working on these subjects thanks to a joined fellowship of the Technion and the French Embassy in Israël.
From 2010 to 2013, I did my Ph.D. at the École Centrale Paris, in the MAS laboratory, under the supervision of professor Erick Herbin. My thesis was primarily focused on the use of a (very!) analytical framework named 2-microlocal analysis in probability theory, and investigate sample path properties of stochastic processes such as multifractional Brownian motion and Lévy processes in this frame. As the former was obviously not cumbersome enough, I happened to mix it with a bit of multifractal analysis to study nice classes of processes such linear fractional stable motion. For epsilon lovers and fans of fractional operators, you may find the full manuscript here.
Before my short academic life, I obtained in 2010 a MSc degree in Probability and Statistics from University Paris XI - Orsay. I also graduated from the engineering school École Centrale Paris with a MSc in Applied Mathematics during the same year.
A full C.V. is also available here.
What I enjoy working on
Probability theory • fractal geometry • local regularity • 2-microlocal analysis • multifractal analysis • (multi)fractional processes • continuous random trees • superprocesses
What I wrote
My research projects in probability theory led to the following publications and preprints the last few years (see the Publications page for more details).
- Paul Balança. Uniform multifractal structure of stable trees. Submitted, 2016.
- Paul Balança and Leonid Mytnik. Singularities of stable super-Brownian motion. Preprint, 2016.
- Paul Balança. Image sets of fractional Brownian sheets. Submitted, 2015.
- Paul Balança. Some sample path properties of multifractional Brownian motion. Stochastic Process. Appl., 2015.
- Paul Balança. Fine regularity of Lévy processes and linear (multi)fractional stable motion. Electron. J. Probab., 2014.
- Paul Balança. An increment type set-indexed Markov property. J. Theoret. Probab., 2014.
- Paul Balança and Erick Herbin. A set-indexed Ornstein-Uhlenbeck process. Electron. Commun. Probab., 2012.
- Paul Balança and Erick Herbin. 2-microlocal analysis of martingales and stochastic integrals. Stochastic Process. Appl., 2012.
I also spent some time working on medical image processing during an internship in the Computational Biomedicine Lab, University of Houston.
- D. Chittajallu, P. Balança and I. Kakadiaris. Automatic delineation of the inner thoracic region in non-contrast CT data. Engineering in Medicine and Biology Society (EMBC). Annual International Conference of the IEEE, 2009.
- R. Yalamanchili, D. Chittajallu, P. Balança, B. Tamarappoo, D. Berman, D. Dey and I. Kakadiaris. Automatic segmentation of the diaphragm in non-contrast CT images. From Nano to Macro, 2010 IEEE International Symposium on Biomedical Imaging, 2009.
Finally, you may also find short articles I have written for the Bulletins Électroniques of the French embassy on science discoveries and technologies news in Israel.
Where I have been
- Porquerolles - Fractals and Related Fields III (Sep. 2015)
- Oxford - 38th Conference on Stochastic Processes and their Applications (July 2015)
- Technion - Stochastic Processes and Random Fields: Geometry and Fine properties (June 2015)
- Technion - Probability seminar (May 2015)
- Weizmann Institute - Students Probability Day V (May 2015)
- Orléans - GDR d’analyse multifractale (Sept. 2014)
- Saint Flour - Probability summer school (July 2014)
- BIRS/Banff - Multifractal Analysis Workshop (Feb. 2014)
- Paris Descartes - Groupe de travail en Probabilités (Oct. 2013)
- Wrocław - 7th International Conference on Lévy Processes (July 2013)
- Orléans - Journées de Probabilités (Juin 2013)
- Paris-Est Créteil - Séminaire Cristolien d’Analyse Multifractale (Mai 2013)
- Istanbul - 8th World Congress in Probability and Statistics (July 2012)
What I have been teaching
- 2010 - 2013: Teaching assistant at École Centrale Paris in Analysis, Probability and Statistics.
- 2013: Teaching assistant at ENSAE in Functional Analysis.
- 2014: Crash course at the Technion on continuous Lévy trees.