Seminar in applied mathematics and statistics
SPEAKER: Andrea Macrina (UCL)
TITLE: Multiple Barrier-Crossings of an Ornstein-Uhlenbeck Diffusion in Consecutive Periods
ABSTRACT: We investigate the joint distribution and the multivariate survival functions for the maxima of an Ornstein-Uhlenbeck (OU) process in consecutive time-intervals. A PDE method, alongside an eigenfunction expansion is adopted, with which we first calculate the distribution and the survival functions for the maximum of a homogeneous OU-process in a single interval. By a deterministic time-change and a parameter translation, this result can be extended to an inhomogeneous OU-process. Next, we derive a general formula for the joint distribution and the survival functions for the maxima of a continuous Markov process in consecutive periods. With these results at hand, one may obtain semi-analytical expressions for the joint distribution and the multivariate survival functions for the maxima of an OU-process, with piecewise constant parameter functions, in consecutive time periods. The joint distribution and the survival functions may be evaluated numerically by an iterated quadrature scheme. This mathematical problem is of relevance in the context of heatwaves, in particular when one is interested in calculating the probability that a heatwave strikes. The focus of this talk shall be on understanding the mathematical complexity of this problem and the numerical challenges faced when implementing the derived results.
Friday, May 24 at 13.15: Amit Mitra
Friday, May 24 at 14.15: Sharmishtha Mitra
Wednesday, May 29 at 15.15: Frank van der Meulen