MAC-MIGS Deep Dive on Stochastic Partial Differential Equations – 12th/13th March
We are pleased to invite PhD students and members of staff to attend a MAC-MIGS Deep Dive in Stochastic Partial Differential Equations with Prof. Stig Larsson (Chalmers University of Technology in Gothenburg).
There will be two introductory lectures, a research seminar, and an opportunity to discuss with the speaker. Registration is required: here
Details and timetable are below. Note different locations.
All talks by Prof. Stig Larsson
Tuesday 12th March
| 11.00-13.00 | Numerical methods for SPDE: strong and weak convergence analysis (Lecture 1) | OSH_G10 – Drummond Library |
| 13.00-14.00 | Lunch | Bayes 5th floor |
Tuesday afternoon chat at Bayes 5th floor (5.45) 15.00-16.00
Wednesday 13th March
| 11.00-13.00 | Numerical methods for SPDE: strong and weak convergence analysis (Lecture 2) | MST_Teaching Room 08 (1.420) – Doorway 3 |
| 13.00-14.00 | Lunch | Bayes 5th floor |
| 15.00-16.00 | Riccati equations for boundary control and filtering of parabolic SPDE: solution theory (ACM seminar) | 40GS_Lecture Theatre A |
Organisers: Abdul-Lateef Haji-Ali and Kostas Zygalakis
Abstracts
Lectures
Strong convergence refers to convergence with respect to a norm, for example, mean square convergence. Proofs typically involve representation of the error using the semigroup theory or energy estimates and using the Ito isometry or the Burkholder–Davies–Gundy inequality.
Weak convergence involves the error in some functional of the solution. Proofs may involve representation of the weak error in terms of the Kolmogorov equation and may use integration by parts from the Malliavin calculus.
- Stochastic integration in Hilbert space. Stochastic evolution problem in Hilbert space. Semigroup, mild solution. Stochastic heat equation. Stochastic wave equation.
- Numerical approximation by finite elements and Euler’s method. Strong convergence.
- Weak convergence. Malliavin calculus.
- Stochastic Cahn-Hilliard equation. (Time permitting.)
ACM Seminar
An abstract solution theory for the operator Riccati equation related to parabolic stochastic partial differential equations is provided. The assumptions on the coefficient operators in the equation apply to a range of applications, including boundary control of linear stochastic evolution equations driven by not necessarily trace-class, linear,
multiplicative, Gaussian noise, and filtering with point observation, non trace-class noise and non-smooth initial value. The theory unifies and extends the generality of previous works, e.g., with respect to the irregularity of the noise and by the inclusion of control noise in the case of control. Detailed regularity results for the solution are
provided.
This is joint work with Adam Andersson and Boualem Djehiche.