Stopping times with given laws

Abstract

Given a stochastic process Xt, t ∈ T ⊂ R, and s ∈ R, then a) iff b): a) For every probability measure μ on [s, ∞], there is a stopping time τ for Xt with law L(τ)=μ; b) If At is the smallest σ-algebra for which Xu are mesurable for all u≤t, then P restricted to At is nonatomic for all t>s.