# Alexander Aurell: Topics in the mean-field type approach to pedestrian crowd modeling and conventions.

**Time: **
Fri 2019-12-06 11.00 - 12.00

**Location: **
F11

**Lecturer: **
Alexander Aurell, KTH

### Abstract

In this talk, I will present selected parts of my thesis, primarily addressing topics in pedestrian crowd modeling and the formation of conventions.

The thesis consists of five papers. The first paper generalizes a pedestrian crowd model for competing subcrowds to include nonlocal interactions and an arbitrary (but finite) number of subcrowds.

The second paper suggest a model for pedestrians with a pre-determined target they have to reach. The fixed and non-negotiable final target leads us to formulate a model with backward stochastic differential equations of mean-field type.

The third paper introduces sticky reflected stochastic differential equations with boundary diffusion as a means to include walls and obstacles. The proposed dynamic model allows the pedestrians to move and interact while spending time on the boundary.

The fourth paper treats two-player finite-horizon mean-field type games between players whose state trajectories are given by backward stochastic differential equations of mean-field type. The paper validates the stochastic maximum principle for such games.

The fifth paper treats the formation of conventions in a large population of agents that repeatedly play a finite two-player game.