Spatial-temporal rainfall models based on poisson cluster processes

Stochastic Models of Spatial and Temporal Distribution of Thunderstorm Rainfall

A simplified stochastic model based on airmass thunderstorm rainfall data from the 58-square-mile Walnut Gulch Experimental Watershed in south eastern Arizona is being developed at the Southwest Watershed Research Center, Tucson, Ariz. Records from the 95 rain gage network on this watershed pro vide valuable information on airmass thunderstorm rainfall in the Southwestern United States. Proba b...

Spatial and Temporal Rainfall Approximation Using Additive Models

Transforming spatial point processes into Poisson processes

In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter point process into a planar Poisson process of unit rate, using random stopping sets. Merzbach and Nualart's theorem applies only to a special class of point processes, since it requires two restrictive conditions: the (F4) condition of conditional independence and the convexity of the 1-compensator. The (F4) co...

Thinning spatial point processes into Poisson processes

This paper describes methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where one simulates backwards and forwards in order to obtain the thinned process. In the case...

Large Deviations of Poisson Cluster Processes

Poisson cluster processes are one of the most important classes of point process models (see Daley and Vere-Jones[7] and Møller; Waagepetersen[24]). They are natural models for the location of objects in the space, and are widely used in point process studies whether theoretical or applied. Very popular and versatile Poisson cluster processes are the so-called self-exciting or Hawkes processes ...