Characterisation of long memory and asymptotic behaviour in linear stochastic functional differential equations, with applications to mathematical finance
by
John Appleby
Dublin City University
Coauthors: Markus Riedle and Xuerong Mao

A question which has been open in the theory of stochastic equations with delay for around 25 years is: what conditions on the coefficients of a linear stochastic differential equation with delay are necessary and sufficient for the asymptotic stability of solutions? In the talk a simple proof is supplied in the mean square case for a one-dimensional linear equation with bounded delay. Results are also presented for equations with unbounded memory and for Volterra equations. The results also enable exact rates of growth and decay of solutions to be determined for all these classes of equation. Applications of these results to mathematical finance are also considered.

Date received: March 30, 2007