arXiv subjects
Publications and source records attributed to P. Spreij.
We propose two classes of dynamic versions of the classical Erdős-Rényi graph: one in which the transition rates are governed by an external regime process, and one in which the transition rates are periodically resampled. For both models we consider the evolution of the number of edges present, with explicit results for the corresponding moments, functional central limit theorems and large deviations asymptotics.
We propose a two-step algorithm for the construction of a Hidden Markov Model (HMM) of assigned size, i.e. cardinality of the state space of the underlying Markov chain, whose $n$-dimensional distribution is closest in divergence to a given distribution. The algorithm is based on the factorization of a pseudo Hankel matrix, defined in terms of the given distribution, into the product of a tall and a wide nonnegative matrix. The implementation is based on the nonnegative matrix factorization (NMF) algorithm. To evaluate the performance of our algorithm we produced some numerical simulations in the context of HMM order reduction.