This paper studies cyclic long‐memory processes with Gegenbauer‐type spectral densities. For a semiparametric statistical model, new simultaneous estimates for singularity location and long‐memory parameters are proposed. This generalized filtered method‐of‐moments approach is based on general filter transforms that include wavelet transformations as a particular case. It is proved that the estimates are almost surely convergent to the true values of parameters. Solutions of the estimation equations are studied, and adjusted statistics are proposed. Monte‐Carlo study results are presented to confirm the theoretical findings.
Consider a symmetric bilinear form E . defined on C c (R d ) byIn this paper we study the stochastic process associated with the smallest closed markovian extension of (E . , C c ), and give a new proof of Markov uniqueness (i.e. the uniqueness of a closed markovian extension) based on purely probabilistic arguments. We also give another purely analytic one. As a consequence, we show that all invariant measures are reversible, provided they are of finite energy. The problem of uniqueness of such measures is also partially solved.
AcademicPress, Inc.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.