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December 2014 Finite-dimensional distributions of a square-root diffusion
Michael B. Gordy
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J. Appl. Probab. 51(4): 930-942 (December 2014).

Abstract

We derive multivariate moment generating functions for the conditional and stationary distributions of a discrete sample path of n observations of a square-root diffusion (CIR) process, X(t). For any fixed vector of observation times t1,...,tn, we find the conditional joint distribution of (X(t1),...,X(tn)) is a multivariate noncentral chi-squared distribution and the stationary joint distribution is a Krishnamoorthy-Parthasarathy multivariate gamma distribution. Multivariate cumulants of the stationary distribution have a simple and computationally tractable expression. We also obtain the moment generating function for the increment X(t + δ) - X(t), and show that the increment is equivalent in distribution to a scaled difference of two independent draws from a gamma distribution.

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Michael B. Gordy. "Finite-dimensional distributions of a square-root diffusion." J. Appl. Probab. 51 (4) 930 - 942, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 1326.60115
MathSciNet: MR3301280

Subjects:
Primary: 60G17
Secondary: 60E10

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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