Speaker: Yushi Hamaguchi
Affiliation: Osaka University, Japan


Solutions of stochastic Volterra integral equations (SVIEs) are neither Markovian nor semimartingales, and thus the usual It\^{o}'s calculus cannot be applied to SVIEs directly. In this talk, we introduce a new framework of Markovian lifts of SVIEs and show that the solution of an SVIE is represented by the solution of a lifted stochastic evolution equation (SEE) defined on a Hilbert space. Our framework can be a useful tool to study SVIEs by means of It\^{o}'s stochastic calculus in Hilbert spaces. Furthermore, we establish an asymptotic log-Harnack inequality for the Markov semigroup associated with the lifted SEE and show some important consequent properties including the uniqueness of the invariant probability measure for the lifted SEE.

About Statistics, modelling and operations research seminars

Students, staff and visitors to UQ are welcome to attend our regular seminars.

The events are jointly run by our Operations research and Statistics and probability research groups.

The Statistics, modelling and operations research (SMOR) Seminar series seeks to celebrate and disseminate research and developments across the broad spectrum of quantitative sciences. The SMOR series provides a platform for communication of both theoretical and practical developments, as well as interdisciplinary topics relating to applied mathematics and statistics.


Zoom only (https://uqz.zoom.us/j/85172010876)