• Corpus ID: 256080847

On the construction and identifcation of Boltzmann processes

  title={On the construction and identifcation of Boltzmann processes},
  author={Sergio Albeverio and Barbara Rudiger and P. Sundar},
Given the existence of a solution { f ( t, x, v ) } t ≥ 0 of the Boltzmann equation for hard spheres, we introduce a stochastic differential equation driven by a Poisson random measure that depends on f ( t, x, v ). The marginal distributions of its solution solves a linearized Boltzmann equation in the weak form. Further, if the distributions admit a probability density, we establish, under suitable conditions, that the density at each t coincides with f ( t, x, v ). The stochastic process is… 

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Itô formula for stochastic integrals w.r.t. compensated Poisson random measures on separable Banach spaces

  • B. RüdigerG. Ziglio
  • Mathematics
  • 2006
We prove the Ito formula (1.3) for Banach valued functions acting on stochastic processes with jumps, the martingale part given by stochastic integrals of time dependent Banach valued random