Random measures on the Brownian path with prescribed expectation

Let B denote the range of the Brownian motion in R^d. For a deterministic Borel measure nu we wish to find a random measure mu such that the support of mu is contained in B and the expectation of mu is nu. We discuss when exactly can there be such a random measure and construct in those cases. We establish a formula for the expectation of the double integral with respect to mu, which is a strong tool for the geometric measure theory of the Brownian path.

• Speaker: Abel Farkas (Rényi Institute, Budapest)
• Tuesday 28 April 2020, 14:00–15:00
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.