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

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.

Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes

In Palm theory it is very common to consider several distributions to describe the characteristics of the system.To study a stationary marked point process, the time-stationary distribution P and its event-stationary Palm distributions P 0 L with respect to sets L of marks can all be used as starting point.When P is used, a modi ed, event-stationary version Q 0 L of P 0 L is de ned as the limit of an obvious discrete-time Ces aro average.In a sense this modi ed Palm distribution is more natural than the ordinary one.When a Palm distribution P 0 L 0 is taken as starting point, we can approximate another modi ed, event-stationary version of P 0 L by considering discrete-time Ces aro averages and a modi ed, time-stationary version QL of P by considering continuous-time Ces aro averages.These and other limit results are corollaries of uniform limit theorems for Ces aro averaged functionals.In essence, this paper presents a profound study of the relationship between P; P 0 L ; P 0 L 0, and modi ed versions of them, and their connections with ergodicity conditions and long-run averages of Ces aro type

Uniform limit theorems for marked point processes

Stochastic Processes;Limit Theorems;60G10;60F15;60G55;probability theory

Bridging the gap between a stationary point process and its palm distribution

Stationary Point;probability theory

Central limit theorems for sequences with M(N)-dependent main part

Probability;probability theory

Integrated Timber Allocation and Transportation Planning in Ireland

Coillte Teoranta, the Irish Forestry Board, was established as a forestry company in 1989, with a mandate to operate in forestry and related activities in a commercial manner. The company took over the assets of the state Forest Service and now owns and manages approximately 400,000 ha of forest. Coillte harvests and sells timber to the private wood processing industries in Ireland. Coillte harvested approximately 1.4 million m3 of timber in 1990. By 2010 this annual harvest volume will increase to 3.5 million m3. In order to manage the harvesting and transportation operations efficiently, a national timber sales allocation procedure was developed by the Forestry Department of University College, Dublin. The procedure uses Coillte's databases on harvest volumes, subdivided into supply categories; on mill demands, specified by demand categories; and on the national transportation network, including road, rail and water transport modes. The developed operational procedure was used as a decision-making tool during the allocation of the 1991 sales volumes. A comparison of the actual versus the optimized 1990 allocation strategy identified opportunities for large-scale savings. In addition to its main function as a decision-making tool for the annual sales allocation, the model has been used for other strategic and tactical planning analyses, such as the influence of new mill location on transport costs, the impacts of a timber processing industry rationalization programme on the industry as a whole and on individual mills, the feasibility of timber transport by rail, the selection of suitable ports for timber export, and the impact of road construction and improvement programmes on national timber transport strategies. The model has been successfully linked with the company's ARC/ INFO Geographic Information System which extends the post-allocation analysis and interpretation capabilities, and combines the output with existing information systems. A further integration of the procedure in the management decision-making processes in the company will result in increased cost saving opportunities

Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space

We apply the perturbation theory integral representation (PTIR) to solve for the bound state Bethe-Salpeter (BS) vertex for an arbitrary scattering kernel, without the need for any Wick rotation. The results derived are applicable to any scalar field theory (without derivative coupling). It is shown that solving directly for the BS vertex, rather than the BS amplitude, has several major advantages, notably its relative simplicity and superior numerical accuracy. In order to illustrate the generality of the approach we obtain numerical solutions using this formalism for a number of scattering kernels, including cases where the Wick rotation is not possible.Comment: 28 pages of LaTeX, uses psfig.sty with 5 figures. Also available via WWW at http://www.physics.adelaide.edu.au/theory/papers/ADP-97-10.T248-abs.html or via anonymous ftp at ftp://bragg.physics.adelaide.edu.au/pub/theory/ADP-97-10.T248.ps A number of (crucial) typographical errors in Appendix C corrected. To be published in Phys. Rev. D, October 199