Chapter 6 opens with extensions of martingale theory in two directions: to σ-finite measures and to random variables with values in a Banach space. In §6.2 I prove Burkholder’s Inequality for ...

To stimulate through theory and examples, an interest and appreciation of the power of the elegant method of martingales in probability theory. Unit description First, rigorous foundations and ...

Section 7.1 provides a brief introduction to the theory of martingales with a continuous parameter. As anyone at all familiar with the topic knows, anything approaching a full account of this theory ...

This course provides instruction in advanced topics in probability and mathematical statistics, mainly based on martingale theory. It is a continuation of Probability and Mathematical Statistics I.

This course deals with probabilistic methods and with various analytic tools used and exploited in probability theory. It builds on the rigorous foundations given in the Martingale Theory with ...

The theory of optimal transport (OT ... transport problem with additional stochastic constraints have received increasing attention, e.g. martingale optimal transport (MOT) and causal/adapted optimal ...