Title: A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff,
Abstract: We consider the spatially homogeneous Boltzmann equation for hard potentials
with angular cutoff. This equation has a unique conservative weak solution
$(f_t)_{t\geq 0}$, once the initial condition $f_0$ with finite mass and energy
is fixed. Taking advantage of the energy conservation, we propose a recursive
algorithm that produces a $(0,\infty)\times\mathbb{R}^3$ random variable
$(M_t,V_t)$ such that $E[M_t {\bf 1}_{\{V_t \in \cdot\}}]=f_t$. We also write
down a series expansion of $f_t$. Although both the algorithm and the series
expansion might be theoretically interesting in that they explicitly express
$f_t$ in terms of $f_0$, we believe that the algorithm is not very efficient in
practice and that the series expansion is rather intractable. This is a tedious
extension to non-Maxwellian molecules of Wild's sum and of its interpretation
by McKean.