Dissertation: Representations and Regularity of Gaussian Processes

Posted on 17/08/15.

Adil Yazigi's dissertation is about Gaussian processes, their representations and regularity.

Yazigi studies the regularity of the sample paths of Gaussian processes and gives a necessary and sufficient condition for Hölder continuity.

Secondly, he introduces the canonical Volterra representation for self-similar Gaussian processes based on the Lamperti transformation and on the canonical Volterra representation of stationary Gaussian processes. The necessary and sufficient condition for the existence of this representation is the property of pure non-determinism which is a natural condition for stationary as well as self-similar Gaussian processes.

Later, Yazigi applies this result to define the class of Gaussian processes that are self-similar with same index and are equivalent in law.

Finally, he investigates the Gaussian bridges in a generalized form where the Gaussian processes are conditioned to multiple final values. The generalized Gaussian bridge will be given explicitly in the orthogonal and the canonical representation where both cases of martingale and non-semimartingale will be treated separately. He will also derive the canonical representation of the generalized Gaussian bridge for invertible Gaussian Volterra processes.

Gaussian bridge model and insider trading

As an application to Finance, he uses the generalized Gaussian bridge model to analyse and to solve the insider trading problem.

– Given a financial market where an insider trader knows at the beginning of the time the final value of a specific asset, the Gaussian bridge model can explain how the price of this asset moves from the randomness to the certainty in the insider agent's point of view, says Adil Yazigi.

Public Defence

The public examination of FM Adil Yazigi's doctoral dissertation”Representations and regularity of Gaussian Processes” will be on Friday 21 August at 12 o´clock in auditorium Kurtén (Tervahovi). Professor Ciprian A. Tudor (Université de Lille) will act as opponent and Professor Tommi Sottinen as a custos.

Publication orders and pdf:

Further information: Adil Yazigi, p. 044 34 55 064, e-mail: firstname.lastname@uva.fi



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