1. Let (2, F, P) be a probability space with a filtration F = (Fn)n20.(a) Let 71, 72 be two F-stopping times. Prove thatT1 A 72 = min(T1, T2)T1 VT2 = max(T1, T2)are both stopping times.(b) Let 7 be an F-stopping time. Prove that 7+1 is also an F-stopping time.

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1. Let (2, F, P) be a probability space with a filtration F = (Fn)n20- (a) Let 71, 72 be two F-stopping times. Prove that T1 A 72 = min(71, 72) T1 VT2 := max(T1, T2) are both stopping times. (b) Let 7 be an F-stopping time. Prove that 7 + 1 is also an F-stopping time.

1. Let (2, F, P) be a probability space with a filtration F = (Fn)n20- (a) Let 71, 72 be two F-stopping times. Prove that T1 A 72 = min(71, 72) T1 VT2 := max(T1, T2) are both stopping times. (b) Let 7 be an F-stopping time. Prove that 7 + 1 is also an F-stopping time.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 20E

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Question

1. Let (2, F, P) be a probability space with a filtration F = (Fn)n20.
(a) Let 71, 72 be two F-stopping times. Prove that
T1 A 72 = min(T1, T2)
T1 VT2 = max(T1, T2)
are both stopping times.
(b) Let 7 be an F-stopping time. Prove that 7+1 is also an F-stopping time.

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