Study of a stochastic model of the ``dangling spider'' problem with an infinite previous history and Poisson switchings (Q5951286)

The paper deals with a stochastic integro-differential equation defined by an external Gaussian white noise and the integral of a Poisson measure which pictures an infinite previous history. By using Picard's method, one can prove the existence and the uniqueness of the solution, but to this end, one has to use an alternative to the classical Gronwall's estimate which does not work here. Then one studies the stability of the solution of this equation: it is shown that the second Lyapunov method applies, and one constructs Lyapunov functionals.