The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.
Speaker at 10:00: Olena Tymoshenko (Igor Sikorsky Kyiv Polytechnic Institute)
Title: The exact order of growth of a solution in some classes of non-homogeneous stochastic differential equation
Abstract: Almost sure asymptotic behaviour of the solution of the non-homogenous stochastic differential equation is considered in the talk. Sufficient conditions, under which the exact order of growth of a solution non-homogenous stochastic differential equation is determined almost surely by a solution of the corresponding ordinary differential equation are obtained. As an application of these results, the problem of \(\phi\)-asymptotic equivalence for solutions of the stochastic differential equation is discussed.
Speaker at 11:00: Kjetil Røysland (Univerity of Oslo)
Title: Estimating clinical treatment effects using stochastic differential equations
Abstract: The standard method for evaluating the effect of a clinical treatment is to carry out some sort of a randomised controlled trial. In a properly designed randomised trial one can trust that the estimated differences between the exposed individuals and their controls represent true causal effects, not subject to confounding, selection bias etc. Such trials however are often difficult to carry out, either because of the required resources, possible ethical considerations, or simply because it would take too much time. An alternative approach is to use non-randomised observations from health registries etc. to model ideal randomised controlled trials, and then use these models to evaluate the effects from various hypothetical treatment regimes. This strategy has turned into a huge area of research called causal Inference.
I will discuss how stability theory for stochastic differential equations can be used to construct consistent estimators of such causal effects based on clinical time-to-event data. I will furthermore discuss how Le Cams theory of semi-parametric statistical estimation leads to a differential calculus in our models, where the tangents are formed by counting process martingales, and how it can be used to construct optimal estimators of clinical treatments.
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.