1. Prove that every stochastic process {X(t), t ∈ T} with a constant trend function and independent increments which satisfies E(|X(t)|) , is a martingale. 2. Let L be a stopping time for a stochastic...

1. Prove that every stochastic process {X(t), t ∈ T} with a constant trend function and independent increments which satisfies E(|X(t)|), is a martingale.

2. Let L be a stopping time for a stochastic process {X(t), t ∈ T} in discrete or continuous time and z a positive constant. Verify that L ∧ z = min (L, z) is a stopping time for {X(t), t ∈ T}.