= Squared Bessel process
{title2=$dZ_t=2\sqrt{Z_t}\,dB_t+\delta\,dt$}
A squared Bessel process of dimension $\delta\ge0$ is a nonnegative continuous solution of the displayed <stochastic differential equation>. It extends the squared radial part of integer-dimensional <Brownian motion> to arbitrary nonnegative dimensions. Before hitting zero its square root solves $dR=dB+(\delta-1)(2R)^{-1}dt$. At dimension zero, a process started at zero remains there. The coefficients are not Lipschitz at zero, so positivity or uniqueness must not be justified by a global Lipschitz theorem.
Back to article page
