A TUTORIAL INTRODUCTION TO STOCHASTIC ANALYSIS …
1.9 Exercise: Every nonnegative local martingale is a supermartingale. 1.10 Exercise: If Xis a submartingale and τis a stopping time, then the stopped process Xτ t 4= X τ∧t, 0 ≤ t<∞ is also a submartingale. 1.11 Exercise (optional sampling theorem): If X is a submartingale with right-
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