Generalized Hamilton system is defined by generalized Poisson bracket, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion,. In the paper, Combinatorial operator η in 1-form space ( ) P Λ on Poisson manifold P is constructed and sufficient and necessary conditions that the vector field which induced by 1-form is...

The theory of sparse stochastic processes offers a broad class of statistical models to study signals. In this framework, signals are represented as realizations of random processes that are solution of linear stochastic differential equations driven by white Lévy noises. Among these processes, generalized Poisson processes based on compoundPoisson noises admit an interpretation as random L-spl...

The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional stati...

The space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We introduce a generalized process by suitably time-changing a superposition of weighted space-fractional Poisson processes. This generalized process can be related t...