Online Workshop on

Stochastic Analysis and Hermite Sobolev Spaces

21–26 June 2021

Aims and scope

The goal of the workshop is to expose research scholars, post doctoral fellows and young faculty to a few techniques that have been developed recently in the context of stochastic processes taking values in the Hermite-Sobolev spaces. This includes the following topics:

• Monotonicity inequality and uniqueness of solutions for SPDEs
• Translation invariance of solutions to SPDEs
• Connections to Geometry, invariant submanifolds
• Applications to Finance and Machine learning
• Applications to Stochastic Analysis & PDEs

While we shall assume basic knowledge of stochastic calculus, we shall also develop in some detail the necessary topics in distribution theory and stochastic integration in finite dimensions and later on, in Hilbert spaces.

The Hermite-Sobolev spaces describe the countably Hilbertian Nuclear topology of the Schwartz space of rapidly decreasing smooth functions; their duals provide a convenient framework for the study of Stochastic PDEs, including Stochastic Differential Equations in finite dimensions.

Recent developments suggest a broader range of applications for these techniques. This is also a motivation for the workshop, which will include lectures by experts in stochastic analysis with the goal of formulating and solving new problems in the framework of Hermite-Sobolev spaces.

Organizers

• Rajeev Bhaskaran (Indian Statistical Institute, Bangalore Centre, India)
• Suprio Bhar (Indian Institute of Technology Kanpur, India)
• Stefan Tappe (Albert Ludwig University of Freiburg, Germany)

The workshop is partially supported by the Science and Engineering Research Board (SERB), India
(vide grant CRG/2019/002594).