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- Olav Kallenberg
- SIAM Review
- 1993

- Olav Kallenberg
- 1973

A random measure ~ defined on some measurable space (S,S) is said to be symmetrically distributed with respect to some fixed measure w on S, if the distribution of (~Al, ... ,~Ak) for kEN and disjoint AI" .. ,AkES only depends on (wAl, ... ,wAk). The first purpose of the present paper is to extend to such random measures (and then even improve) the results… (More)

Let ξ be a Dawson–Watanabe superprocess in R such that ξt is a.s. locally finite for every t ≥ 0. Then for d ≥ 2 and fixed t > 0, the singular random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of supp ξt. When d ≥ 3, the local distributions of ξt near a hitting point can be approximated… (More)

- Olav Kallenberg
- 2010

Given a probability space (Ω,A, P ) and some σ-fields F ,G ⊂ A, we consider iterated conditional distributions of the form (P [ · | F ])[ · | G]. Thus, in the second step, we form the conditional distribution with respect to G, using P [ · |F ] instead of P as the underlying probability measure. Under suitable regularity conditions, we show that… (More)

- Olav Kallenberg
- 2012

- Peter Bickel, Olav Kallenberg, +13 authors Anton J. Flugge
- 2016

- Olav Kallenberg
- 2008

Let ; and n be point processes and let p€[O,I]. We say that ; is a p-thinning of n, if it is obtained from n by deleting the atoms independently with probability l-p. It is shown that, if PI,P2, ... €(O,I] with P +0 n and if ; n is a p -thinning of some n for each n€N, then ~n converges in distribution in the vague topology if and only if Pnnn does.… (More)

- Olav Kallenberg
- 2008

PREFACE Random measure theory is a new and rapidly growing branch of probabi li ty of increasing interest both in theory and applications. Loosely speaking, it is concerned with random quantities which can only take non-negative values, such as e.g. the number of random variables in a given sequence possessing a certain property, the time spent by a random… (More)

- Olav Kallenberg
- 2008

We explain how invariance in distribution under separate or joint contractions, permutations, or rotations can be defined in a natural way for d-dimensional arrays of random variables. In each case, the distribution is characterized by a general representation formula, often easy to state but surprisingly complicated to prove. Comparing the representations… (More)

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