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April, 1973 A Continuum of Collision Process Limit Theorems
Richard Gisselquist
Ann. Probab. 1(2): 231-239 (April, 1973). DOI: 10.1214/aop/1176996976


Let $\{x_i(t): i = \cdots -1, 0, 1, \cdots\}$ be a collection of one-dimensional symmetric stable processes of order $\gamma \in (0, 1\rbrack$ with the property that the starting positions $\cdots < x_{-1}(0) < x_0(0) = 0 < x_1(0) < \cdots$ form a Poisson system with rate one. By generalizing the order preserving property of elastic collision, these can be used to define a set of collision processes $\{y_i(t)\}$. It is shown in this paper that for large values of $A$, the finite dimensional distributions of $y_0(At)/A^{1/2\gamma}$ approach the Gaussian distribution with mean zero and covariance $r(t, s) = c(t^{1/\gamma} + s^{1/\gamma} - |t - s|^{1/\gamma})$.


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Richard Gisselquist. "A Continuum of Collision Process Limit Theorems." Ann. Probab. 1 (2) 231 - 239, April, 1973.


Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0263.60047
MathSciNet: MR373069
Digital Object Identifier: 10.1214/aop/1176996976

Primary: 60F05
Secondary: 60G15 , 60J30

Keywords: interactions of stochastic processes , limit theorems , Stochastic processes

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 2 • April, 1973
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