Week 08.03.2026 – 14.03.2026

Quantum stochastic calculus is a beautiful theory that flows ineluctably from its classical counterpart. We will start with the basic idea of a normal martingale and demonstrate this natural development, via multiple Wiener-Ito integrals, chaotic representation, probabilistic interpretations of Boson Fock space and the fundamental quantum stochastic integrators.

Quantum stochastic calculus is a beautiful theory that flows ineluctably from its classical counterpart. We will start with the basic idea of a normal martingale and demonstrate this natural development, via multiple Wiener-Ito integrals, chaotic representation, probabilistic interpretations of Boson Fock space and the fundamental quantum stochastic integrators.

Luke Ayres

Title: Design of experiments on sampled networks.
Abstract:Experiments on social networks are increasingly important, for example, marketing experiments where the effectiveness of different advertisements given to different users needs to be assessed. Development of methods for optimizing the design of experiments on networks is an active area of research. A significant complication is that in networked experiments, the response of a given unit depends not only on the direct treatment applied to that unit, but also on the indirect effect of treatments applied to connected units. Previous research has focused on the problem of optimal design (treatment allocation) to assess direct treatment effects, indirect network effects, or a combination of both. The focus here is on how different network properties, such as edge density, impact different optimality criteria. Studying such properties is particularly important for experiments on large networks where it is likely that not all available units will be used due to cost and/or computation time. Hence, a sub-network will need to be chosen for experimentation, with different choices giving different network properties. The use of different network sampling algorithms is assessed to evaluate the effectiveness of the resulting optimal designs and to demonstrate the important role of network structure in determining design efficiency.

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Carson McKee

Title: Sharing Behaviours between Multiple Time Series with Compound Random Measures
Abstract: This work presents a Bayesian nonparametric approach to pooling information across multiple related time series. We assume that each series can be modelled as a state switching process and is free to switch at different times to others. The states are drawn from an infinite collection of behaviours, with each series exhibiting a subset of these behaviours. This is achieved using vectors of dependent random measures with shared atoms, partic...

See: https://www.londonmathfinance.org.uk/seminar

See: https://www.londonmathfinance.org.uk/seminar