We consider a Poisson process η on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of η. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Itô chaos expansion. We apply these results to extend well-known variance inequal...

In this paper, we consider the problem of mean-variance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem and closed form expressions for the optimal hedging policy are obtained using methods from stochastic control and th...

We study the distribution of discounted collective risk model where the counting process is Poisson. For the model considered here, we obtain mean, variance and moment generating function (m.g.f) of the model. To do this, we use two approaches. In the first approach we use classical methods to obtain the mean and variance. In the second approach we introduce some proper martingale and then we o...

Variance-stabilizing transformations are commonly exploited in order to make non-homoskedastic data easily tractable by standard methods. However, for the most common families of distributions (e.g., binomial, Poisson, etc.) exact stabilization is not possible and even achieving some approximate stabilization turns out to be rather challenging. We approach the variance stabilization problem as ...

This paper deals with the union set of a stationary Poisson process cylinders in Rn having an (n−m)-dimensional base and m-dimensional direction space, where m∈{0,1,…,n−1} n≥2. The concept simultaneously generalises those Boolean model hyperplane or m-flat process. Under very general conditions on typical cylinder Berry-Esseen bound for volume within sequence growing test sets is derived. Assum...

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...

The data-driven Haar-Fisz (DDHF) transformation was recently developed to stabilise the variance of data with an increasing (but otherwise unknown) mean-variance relationship. This report investigates the empirical bias of the DDHF transform and compares it to the much used Box-Cox transformation, using both simulated Poisson counts and data of the deaths of coalition personnel in Iraq.

*Correspondence: [email protected] 1Department of Mathematics, Ohio University, Athens, OH, USA Full list of author information is available at the end of the article Abstract Poisson-Tweedie mixtures are the Poisson mixtures for which the mixing measure is generated by those members of the family of Tweedie distributions whose support is non-negative. This class of non-negative integer-valued ...