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13
Construction of Diffusions on Configuration Spaces
"... We show that any square field operator on a measurable state space E can be lifted by a natural procedure to a square field operator on the corresponding (multiple) configuration space \Gamma E . We then show the closability of the associated lifted (pre)Dirichlet forms E \Gamma ¯ on L 2 (\Ga ..."
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Cited by 27 (3 self)
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We show that any square field operator on a measurable state space E can be lifted by a natural procedure to a square field operator on the corresponding (multiple) configuration space \Gamma E . We then show the closability of the associated lifted (pre)Dirichlet forms E \Gamma ¯ on L 2 (\Gamma E ; ¯) for a large class of measures ¯ on \Gamma E (without assuming an integration by parts formula) generalizing all corresponding results known so far. Subsequently, we prove that under mild conditions the Dirichlet forms E \Gamma ¯ are quasiregular, and that hence there exist associated diffusions on \Gamma E , provided E is a complete separable metric space and \Gamma E is equipped with a suitable topology, which is the vague topology if E is locally compact. We discuss applications to the case where E is a finite dimensional manifold yielding an existence result on diffusions on \Gamma E which was already announced in [AKR96a, AKR96b], resp. used in [AKR98, AKR97b]. Furthermore...
Shot noise Cox processes
 Advances in Applied Probability 35
, 2003
"... We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be ..."
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Cited by 23 (6 self)
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We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby a very large class of models for aggregated or clustered point patterns is obtained. Due to the structure of GSNCPs, a number of useful results can be established. We focus first on deriving summary statistics for GSNCPs and next on how to make simulation for GSNCPs. Particularly, results for first and second order moment measures, reduced Palm distributions, the Jfunction, simulation with or without edge effects, and conditional simulation of the intensity function driving a GSNCP are given. Our results are exemplified for special important cases of GSNCPs, and we discuss the relation to corresponding results for SNCPs.
Simulationbased Inference for Spatial Point Processes
, 2001
"... Introduction Spatial point processes play a fundamental role in spatial statistics. In the simplest case they model \small" objects that may be identied by a map of points showing stores, towns, plants, nests, galaxies or cases of a disease observed in a two or three dimensional region. The points ..."
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Cited by 8 (1 self)
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Introduction Spatial point processes play a fundamental role in spatial statistics. In the simplest case they model \small" objects that may be identied by a map of points showing stores, towns, plants, nests, galaxies or cases of a disease observed in a two or three dimensional region. The points may be decorated with marks (such as sizes or types) whereby marked point processes are obtained. The areas of applications are manifold: astronomy, geography, ecology, forestry, spatial epidemiology, image analysis, and many more. Currently spatial point processes is an active area of research, which probably will be of increasing importance for many new applications, as new technology such as geographical information systems makes huge amounts of spatial point process data available. Textbooks and review articles on dierent aspects of spatial point processes include Matheron (1975), Ripley (1977), Ripley (1981), Diggle (1983), Penttinen (1984), Daley &VereJones (1988),
A General Stochastic Model For Nucleation And Linear Growth.
 Ann. Applied Probab
, 1996
"... this paper incorporates both these as special cases and we indicate how to obtain their results. In the third example, attention was focussed on the distances between heterocysts as given by a particular simple model for the inhibitory process. This will be examined under a general model. In the fou ..."
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Cited by 5 (2 self)
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this paper incorporates both these as special cases and we indicate how to obtain their results. In the third example, attention was focussed on the distances between heterocysts as given by a particular simple model for the inhibitory process. This will be examined under a general model. In the fourth example, lengths of crystals were of interest and these also are examined under the general model. In all cases, it is of interest to examine the properties of the number of initiated points, the distances between them, both at the end of the process (at infinite time) and at some intermediate times, when it is also of interest to look at the number and length of gaps (and of covered regions), and the distribution of times to initiation of the process at various points. 1 Consider a two dimensional Poisson process \Xi, on time and level, (t; x),
Analysis on Poisson and Gamma spaces
 HIROSHIMA MATH. J
, 1998
"... We study the spaces of Poisson, compound Poisson and Gamma noises as special cases of a general approach to nonGaussian white noise calculus, see [KSS97]. We use a known unitary isomorphism between Poisson and compound Poisson spaces in order to transport analytic structures from Poisson space to c ..."
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Cited by 4 (0 self)
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We study the spaces of Poisson, compound Poisson and Gamma noises as special cases of a general approach to nonGaussian white noise calculus, see [KSS97]. We use a known unitary isomorphism between Poisson and compound Poisson spaces in order to transport analytic structures from Poisson space to compound Poisson space. Finally we study a Fock type structure of chaos decomposition on Gamma space.
Small scale limit theorems for the intersection local times of Brownian motion
 Electronic J. Probab
, 1999
"... E l e c t r o n ..."
Symmetry Properties of Average Densities and Tangent Measure Distributions of Measures on the Line
, 1996
"... : Answering a question by Bedford and Fisher in [4] we show that for the circular and onesided average densities of a Radon measure on the line with positive lower and nite upper densities the following relations hold almost everywhere D (; x) = D + (; x) = (1=2)D (; x) and D (; x) ..."
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Cited by 3 (3 self)
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: Answering a question by Bedford and Fisher in [4] we show that for the circular and onesided average densities of a Radon measure on the line with positive lower and nite upper densities the following relations hold almost everywhere D (; x) = D + (; x) = (1=2)D (; x) and D (; x) = D + (; x) = (1=2)D (; x) : We infer the result from a more general formula, which is proved by means of a detailed study of the structure of the measure and which involves the notion of tangent measure distributions introduced by Bandt ([2]) and Graf ([9]). We show that for almost every point x the formula Z Z G(; u) d(u) dP () = Z Z G(T u ; u) d(u) dP () holds for every tangent measure distribution P of at x and all Borel functions G : M(IR) IR ! [0; 1). Here T u is the measure dened by T u (E) = (u +E) and M(IR) is the space of Radon measures with the vague topology. By this formula the tangent measure distributions are Palm distribu...