Asymptotic mean stationarity and absolute continuity of point process distributions

This paper relates - for point processes $\Phi$ on $\mathbb{R}$ - two types of asymptotic mean stationarity (AMS) properties and several absolute continuity results for the common probability measures emerging from point process theory. It is proven that $\Phi$ is AMS under the time-shifts if and only if it is AMS under the event-shifts. The consequences for the accompanying two types of ergodic theorem are considered. Furthermore, the AMS properties are equivalent or closely related to several absolute continuity results. Thus, the class of AMS point processes is characterized in several ways. Many results from stationary point process theory are generalized for AMS point processes. To obtain these results, we first use Campbell's equation to rewrite the well-known Palm relationship for general nonstationary point processes into expressions which resemble results from stationary point process theory.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ423 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Dominated Families of Shifted Palm Distributions

In stationary point process theory, the concept Palm distribution plays an important role.Many important results (like for instance Little s law, so important in many fields) arise from it.However, in the non-stationary case a whole family of local Palm distributions (PD s) has to be considered and the concept seems to loose its importance.The present paper mainly considers non-stationary point processes, and studies relations between the distribution P of a point process, the family {Px} of PD s, and the family {P0,x} of shifted PD s.Here P0,x is the probability distribution that is experienced from an occurrence (arrival, point, transaction) at x.It is attempted to regain some of the glance of the concept Palm distribution by considering generalizations of results that are basic for stationary point processes.Starting point is a refined version of Campbell s equation, which expresses the general relationship between the distribution P of the point process and the family {Px} of PD s.It is used to generalize the inversion formula, well known from stationary point process theory.This generalization is basic; it leads to several relations regarding the above distributions.In the second part of the research domination assumptions are imposed: either the null-sets of a time-stationary distribution are also null-sets of P or the nullsets of one event-stationary distribution are also null-sets of almost all shifted PD s.Under such domination regulations, P0,x can explicitly be expressed in terms of P and several stationary-case long-run properties can be generalized.The relationship between the two types of domination assumptions is carefully studied.point processes;non-stationarity;family of Palm distributions;domination

Estimation of the regional evapotranspiration from remotely sensed crop surface temperatures. Grassland

Estimation of the regional evapotranspiration from remotely sensed crop surface temperature

Realizations of interest rate models

In this paper we comment on a recent paper by Bj¨ork and Gombani. In contrast to this paper our starting point is not the Musiela equation but the forward rate dynamics. In our approach we do not need to talk about infinitesimal generators.

Producing space, producing China : a critical intervention

The concepts of the production and representation of space and place are receiving an increasing amount of attention in both the humanities and the social sciences. This paper will use the theoretical knowledge that has and continues to be produced on the subject to come to a better understanding of the spatial origins that constitute the place that is Chinese nation state. The analysis of spatial practises should shed light on the question what China is and wherefrom it receives the legitimacy for its social-spatial integrity. It will be argued that the arrival of modernity and its universal measurement of time and space were essential components in the gradual transformation from ethnocentric place to a territorially defined nation state. The political production and organisation of space employed for the formation of the nation state is argued to be the consequence of the same (globalising) logic that is now said to question and undermine its territorial integrity. Modernity and globalisation are in this paper, in other words, considered to be similar, if not identical, spatial-temporal concepts that both help to create and destruct places. This is arguably best visible in the constant production and reproduction of the most sophisticated of spatial organisations: our cities. I will argue that despite the changing face of cities, of which the disputed contemporary "globalisation" is but one of many, the spatial reality that is the modern nation state remains the same. This is not to return to an orthodox realist interpretation but to understand the very "stuff" that space and place are made of

Solutions of the Wick-Cutkosky model in the Light-Front Dynamics

We study relativistic effects in a system of two scalar particles interacting via a scalar exchange in the Light Front Dynamcis framework. The results are compared to those provided by Bethe-Salpeter and non relativistic equations. It is found in particular that for massive exchange, the relativistic description is of crucial importance even in the limit of zero binding energy. PACS: 11.10, 03.70, 03.65P Keywords: Light-Front Dynamics, Relativistic equations, Quantum Field TheoryComment: 12 pages, 11 figures, Latex.tar.gz file Accepted in Phys. Lett.