= Power diffusion
{title2=$dX_t=X_t^\alpha\,dB_t$}
A power diffusion has a power of its positive state as noise coefficient. Here the normalized zero-drift family is considered on $U=(0,\infty)$ with $X_0>0$. Its coefficients are locally <Lipschitz continuous> on that domain, so a <maximal local solution of a stochastic differential equation> is pathwise unique before its lifetime. The <Lamperti transform> reduces its noise coefficient to a constant; the case $\alpha=1$ is <geometric Brownian motion>. This normalized family is part of the constant-elasticity-of-variance models, but is not the whole model with arbitrary drift and scale.
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