(a) Let 0 , 1 , 2 , be independent r v s and E i 0 for all i Let X 0 0 and X t Z 1 Z t for t 1 where Z k k1 k Are Zs independent Show that X t is a martingale (b) Let E i m 0 Write Doobs decomposition ...

a The neighbor terms Zk k15k and Zk1 Skk1 may be dependent since they contain the common te ...

(a) Let 0 , 1 , 2 , ... be independent r.v.s and E{...

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(a) Let ξ₀, ξ₁, ξ₂, ... be independent r.v.’s and E{ξ_i} = 0 for all i. Let X₀ = 0 and X_t = Z₁+...+Z_t for t ≥1 where Z_k = ξ_k−1ξ_k. Are Z’s independent? Show that X_t is a martingale.

(b)∗ Let E{ξ_i} = m = 0. Write Doob’s decomposition.

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Probability And Stochastic Modeling

ISBN: 9781439872062

1st Edition

Authors: Vladimir I. Rotar

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Question Posted: Jan 11, 2024 09:01 AM

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(a) Let 0 , 1 , 2 , ... be independent r.v.s and E{...

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