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Energy image density property and the lent particle method for Poisson measures
 Jour. of Functional Analysis
"... We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the energy image density property for Dirichlet forms. The associated gradient is a local operator and gives rise to a nice formula called the lent particle method which consists in adding a particle an ..."
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Cited by 6 (4 self)
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We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the energy image density property for Dirichlet forms. The associated gradient is a local operator and gives rise to a nice formula called the lent particle method which consists in adding a particle and taking it back after some calculation.
Uniform Convergence in some Limit Theorems for Multiple Particle Systems
, 1996
"... For n particles di using throughout R (or Rd), let n�t(A), A 2B, t 0, be the random measure that counts the number of particles in A at time t. Itisshown that for some basic models (Brownian particles with or without branching and di usion with a simple interaction) the processes f ( n�t ( ) ; E n�t ..."
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Cited by 2 (0 self)
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For n particles di using throughout R (or Rd), let n�t(A), A 2B, t 0, be the random measure that counts the number of particles in A at time t. Itisshown that for some basic models (Brownian particles with or without branching and di usion with a simple interaction) the processes f ( n�t ( ) ; E n�t ()) = p n: t 2 [0�M] � 2 CL (R)g, n 2 N, converge in law uniformly in (t �). Previous results consider only convergence in law uniform in t but not in. The methods used are from empirical process theory. 1
NONEQUILIBRIUM DENSITY FLUCTUATIONS FOR THE ZERO RANGE PROCESS WITH COLOUR
, 2006
"... Abstract. We examine the fluctuations of the empirical density measure for the colour version of the symmetric nearest neighbour zero range particle systems in dimension one. We show that the weak limit of these fluctuations is the solution of a system of coupled generalized OrnsteinUhlenbeck proce ..."
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Cited by 2 (1 self)
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Abstract. We examine the fluctuations of the empirical density measure for the colour version of the symmetric nearest neighbour zero range particle systems in dimension one. We show that the weak limit of these fluctuations is the solution of a system of coupled generalized OrnsteinUhlenbeck processes. We also discuss how this result may be used to prove a central limit theorem for the tagged particle on the level of finite dimensional distributions, and identify the limiting variance. This is the central limit theorem associated to propagation of chaos for this interacting particle system. 1.
Stationary Systems of Gaussian Processes
, 2009
"... We describe all countable particle systems on R which have the following three properties: independence, Gaussianity, and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson point process with intensity measure m and moving independently of each o ..."
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We describe all countable particle systems on R which have the following three properties: independence, Gaussianity, and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson point process with intensity measure m and moving independently of each other according to the law of some Gaussian process ξ. We describe all pairs (m, ξ) generating a stationary particle system, obtaining three families of examples. One of these families appeared in connection with extremes of independent Gaussian processes in [Z. Kabluchko, M. Schlather, L. de Haan, Stationary maxstable fields associated to negative definite functions, Ann. Probab. (2009), in press].
Time–Localization of Random Distributions on Wiener Space II: Convergence, Fractional Brownian Density Processes *
"... Abstract. For a random element X of a nuclear space of distributions on Wiener space C([0, 1], R d), the localization problem consists in “projecting ” X at each time t ∈ [0, 1] in order to define an S ′ (R d)valued process X = {X(t), t ∈ [0, 1]}, called the timelocalization of X. The convergence ..."
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Abstract. For a random element X of a nuclear space of distributions on Wiener space C([0, 1], R d), the localization problem consists in “projecting ” X at each time t ∈ [0, 1] in order to define an S ′ (R d)valued process X = {X(t), t ∈ [0, 1]}, called the timelocalization of X. The convergence problem consists in deriving weak convergence of timelocalization processes (in C([0, 1], S ′ (R d)) in this paper) from weak convergence of the corresponding random distributions on C([0, 1], R d). Partial steps towards the solution of this problem were carried out in [BG1, BGN], the tightness having remained unsolved. In this paper we complete the solution of the convergence problem via an extension of the timelocalization procedure. As an example, a fluctuation limit of a system of fractional Brownian motions yields a new class of S ′ (R d)valued Gaussian processes, the “fractional Brownian density processes”.
unknown title
, 1997
"... stochastic processes and their applications Uniform convergence in some limit theorems for multiple particle systems ..."
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stochastic processes and their applications Uniform convergence in some limit theorems for multiple particle systems