Exercise 13.8 Let where {z(t)} is a standard Brownian motion. Let n = inf{t > 0 :

Exercise 13.8 Let

where {z(t)} is a standard Brownian motion. Let τn = inf{t > 0 : ez2(t) = n}. Prove that τn → ∞ as n → ∞
and that {M(t)} is a local martingale with the localizing sequence {τn}. Also, prove that

hence {M(t)} is not a martingale.

Transcribed Image Text:

M(t) = fe(s) dz(s),