On a connection between the non-central [chi]2 distribution and Bessel diffusions

The noncentral [chi]2 random variable can be written as the sum of two independent random variables one of which is a (central) [chi]2 random variable and the other is known as the [chi]2 random variable with zero d.f. We give a probabilistic proof of this by using properties of the square of a Bessel diffusion.