This is a reminder for the: STAR Online Seminars.

The seminar will be held Friday 18. December from 11:00-12:00 . You will recieve the link for the Zoom room by registering for the seminar with the link provided at the end of this mail. The lecture will last for 45 minutes + questions.

This week's speaker is Federica Masiero - Università degli Studi di Milano-Bicocca, with the seminar:

Regularizing properties and HJB equations for stochastic problems with delay

Abstract: In this talk we consider stochastic differential equations with delay. It is well known that the Ornstein-Uhlenbeck transition semigroup doesn’t have regularizing properties, such as the strong Feller property. So in general, the associated Hamilton-Jacobi-Bellman (HJB) equation cannot be solved in mild sense by a classical fixed point argument. We present a result of existence of regular solutions for the HJB equations related to a stochastic controlled equation with delay in the control and in the case when, as it often occurs in applications, the objective function depends only on the “present” of the state and control variable. The result is based on partial regularization results for the associated Ornstein-Uhlenbeck semigroup. In analogy, we investigate partial reularizing properties in the case of delay in the state and with a special dependence on the past trajectory, and we solve in mild sense the associated HJB equation and the stochastic controlled problem related. The talk is mainly based on joint works with F. Gozzi and G. Tessitore.

After the end of the seminar, you are invited to bring a cup of coffee/tea and have a chat in our Coffee in the Stars here you will have the chance to talk and interact with the other persons that attended the seminar, and have a digital "coffee break".

We are looking forward to see you, online!

Best regards,

Michele Giordano

Doctoral research fellow

Department of Mathematics

University of Oslo, Norway

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Link for the seminar webpage: https://www.mn.uio.no/math/english/research/projects/storm/events/seminars/star-online-seminars/index.html