​Dear all, It is soon time to kick-off the online seminar series: STAR - STochastics And Risk - Online Seminars. This series of seminars brings together 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 SCROLLER<https://www.mn.uio.no/math/english/research/projects/scroller/index.html>, SPATUS<https://www.mn.uio.no/math/english/research/projects/spatus/>, and STORM<https://www.mn.uio.no/math/english/research/projects/storm/>. If you would like to take part to the seminars series please register here.<https://nettskjema.no/a/159180#/page/1> <https://nettskjema.no/a/159180#/page/1> On Friday 18. September from 11:00-12:00 the first seminar will be held, and after that it will run on a weekly basis. The lecture will last for 45 minutes + questions, and afterwards you are invited to bring a cup of coffee/tea and have a chat in our "Coffe in the Stars". The first speaker is Andreas Petersson, with the seminar: Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs Abstract: We consider the computation of quadratic functionals of the solution to a linear parabolic stochastic partial differential equation (SPDE) with multiplicative Gaussian noise on a bounded domain. The functionals are allowed to be path dependent and the noise is white in time and may be white in space. An operator valued Lyapunov equation, whose solution admits a deterministic representation of the functional of the SPDE solution, is used for this purpose and error estimates are shown in suitable operator norms for a fully discrete approximation of this equation. We also use these estimates to derive weak error rates for a fully discrete approximation of the SPDE itself. In the setting of finite element approximations, a computational complexity comparison reveals that approximating the Lyapunov equation allows us to compute quadratic functionals more cheaply compared to applying Monte Carlo or covariance-based methods directly to the discretized SPDE. We illustrate the theoretical results with numerical simulations. For more details on this event, see: https://www.mn.uio.no/math/english/research/projects/storm/events/seminars/s... There you will find a list of all the speakers, abstracts, and more details about the seminar series. If you register to the seminars series, you will receive a mail with the details for the zoom meeting next week. We are looking forward to see you, online! Best regards, Michele and Giulia ​