Eighth Colloquium on the Qualitative Theory of Differential Equations
نویسندگان
چکیده
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 functional differential equations characterise the mean square stability of the solution? In this talk, a simple proof is supplied for a one-dimensional linear Volterra equation. The arguments extend to equations with finite memory or unbounded memory, and enable exact rates of growth and decay of the mean square of solutions to be determined for these classes of equation. Applications of the results to mathematical finance are also considered. The results in the talk stem from joint work with E. Buckwar (Humboldt), I. Győri (Pannon), X. Mao (Strathclyde, Glasgow), D. Reynolds (DCU, Dublin), and M. Riedle (Humboldt). Proof for a Conjecture of Wright on a Delay Differential Equation – Computer-assisted part Balázs Bánhelyi Universiy of Szeged Hungary Consider the following delayed differential equation:
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