Research and Publications

My research interests and papers.

Research Keywords (In chronological order of the time I have read them)

Levy processes, Stable processes, Self-similar Markov processes, Lamperti-Kiu representations, Markov Additive Processes, Cramer-Esscher-type transforms, Markov Renewal Theorem

Note : I do not own any of the contents linked from the keywords.
Note2 : The font size represents the frequency of the keyword that is mentioned in my previousr paper(s).

Conditioned real-valued self-similar Markov processes

Joint work with Andreas Kyprianou(My PhD supervisor), Victor Rivero

We will be looking to condition a self-similar Markov process to stay in a particular set.

General theme of this problem : Given a martingale that vanished outside a given set. Then, try to show that the tail distribution of the exit time behaves similar to the martingale(normally with the help of Markov Renewal Theorem). Then, deduce that the conditioning actually corresponds to the process Doob-h transformed be the martingale.

More details : Presentation slide in Lille, My paper written with Andreas Kyprianou and Victor Rivero

Predicting Geomagnetic Storms with transition probabilities

Joint work with Nicole Augustin, Andrea Lelli

Electromagnetic storm is a temporary disturbance in the Earth's magnetic fields caused by the activities of the Sun. This could be modelled simply as a discrete time Markov Chain

However, we know that the Geomagnetic storms are caused directly by the Sun. We will be looking to include the information of the Sun activity into our model. See ITT presentation slides

This work is followed from the ITT3 as a project introduced by the Met Office.

People I have written papers with

Andreas Kyprianou(My PhD supervisor), Victor Rivero

Main events update

My first submitted paper

I had my first paper on Conditioned real self-similar Markov processes submitted to arXiv on 6th October 2015. This is my joint work with Andreas Kyprianou and Victor Rivero.

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Sympoisum on Probability and Stochastic Processes, Merida

On November 2015, I have attended the a large Mexican stochastic process symposium. I have also presented my paper on Conditioned self-similar Markov processes

This trip is supported by Santander International Mobility Bursary.

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