An example driven introduction to probabilistic rough paths

Francois Delarue; William Salkeld

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arXiv · 2106.09801

An example driven introduction to probabilistic rough paths

Francois Delarue·William Salkeld

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Abstract

In these notes, we provide an introduction to a new regularity structure used for solving rough mean-field equations. The index set of this regularity structure is described a collection of novel objects which we refer to as Lions trees. These objects arise in Taylor expansions involving the Lions derivative and capture many of the desirable properties of mean-field dynamics. This work represents a comprehensive generalisation of the ideas first introduced in [BCD20] that promise powerful insights into how interactions with a collective determine the dynamics of an individual within this collective.

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Francois Delarue, William Salkeld. 2021-06-17. An example driven introduction to probabilistic rough paths. https://arxiv.org/abs/2106.09801

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