=+9. Let Nt denote the number of random points that occur by time t in a Poisson
Question:
=+9. Let Nt denote the number of random points that occur by time t in a Poisson process on [0, ∞) with intensity λ. Show that the following stochastic processes Xt = Nt − λt Xt = (Nt − λt)
2 − λt Xt = e−θNt+λt(1−e−θ)
enjoy the martingale property E(Xt+s| Nr, r ∈ [0, t]) = Xt for s > 0.
(Hint: Nt+s − Nt is independent of Nt and distributed as Ns.)
266 10. Martingales
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: