Measure changes with extinction

S.C. Harris , M.I. Roberts

We consider a martingale change of measure and clarify that in general is only a supermartingale under . Defining as the extinction time, we then give a necessary and sufficient condition under which the identity holds.

Mots clés: Measure change; Extinction; Martingale; Galton Watson process; Branching Brownian motion

S.C. Harris, M.I. Roberts. Measure changes with extinction. Statistics and Probability Letters, 2009, 79 (8), pp.1129. ⟨10.1016/j.spl.2008.12.025⟩. ⟨hal-00516885⟩