0000000000824045
AUTHOR
R. Höpfner
showing 2 related works from this author
Non-parametric Estimation of the Death Rate in Branching Diffusions
2002
We consider finite systems of diffusing particles in R with branching and immigration. Branching of particles occurs at position dependent rate. Under ergodicity assumptions, we estimate the position-dependent branching rate based on the observation of the particle process over a time interval [0, t]. Asymptotics are taken as t → ∞. We introduce a kernel-type procedure and discuss its asymptotic properties with the help of the local time for the particle configuration. We compute the minimax rate of convergence in squared-error loss over a range of Holder classes and show that our estimator is asymptotically optimal.
Ergodicity for a stochastic Hodgkin–Huxley model driven by Ornstein–Uhlenbeck type input
2013
We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron itself is modeled by a variant of the classical Hodgkin-Huxley model. Using the existence of an accessible point where the weak Hoermander condition holds and the fact that the coefficients of the system are analytic, we show that the system is non-degenerate. The existence of a Lyapunov function allows to deduce the existence of (at most a finite number of) extremal invariant measures for the process. As a consequence, the complexity of the system is drastically reduced in c…