  A famous feature of the Camassa-Holm equation is its admission of peaked
soliton solutions known as peakons. We investigate this equation under the
influence of stochastic transport. Noting that peakons are weak solutions of
the equation, we present a finite element discretisation for it, which we use
to explore the formation of peakons.
  Our simulations using this discretisation reveal that peakons can still form
in the presence of stochastic perturbations. Peakons can emerge both through
wave breaking, as the slope turns vertical, and without wave breaking as the
inflection points of the velocity profile rise to reach the summit.
