  One approach to the analysis of stochastic fluctuations in market prices is
to model characteristics of investor behaviour and the complex interactions
between market participants, with the aim of extracting consequences in the
aggregate. This agent-based viewpoint in finance goes back at least to the work
of Garman (1976) and shares the philosophy of statistical mechanics in the
physical sciences. We discuss recent developments in market microstructure
models. They are capable, often through numerical simulations, to explain many
stylized facts like the emergence of herding behavior, volatility clustering
and fat tailed returns distributions. They are typically queueing-type models,
that is, models of order flows, in contrast to classical economic equilibrium
theories of utility-maximizing, rational, ``representative'' investors.
Mathematically, they are analyzed using tools of functional central limit
theorems, strong approximations and weak convergence. Our main examples focus
on investor inertia, a trait that is well-documented, among other behavioral
qualities, and modelled using semi-Markov switching processes. In particular,
we show how inertia may lead to the phenomenon of long-range dependence in
stock prices.
