Let 1 , 2 , be independent r v s having an exponential distribution, and E i 1 Let S 0 0, St 1 t , and X t C t exp S t , where C t is a constant such that X t is a martingale (a) Find C t (b) Find lim t X t How fast is such a convergence ...

a First Ee fo e e dx The reader who did not skip Chapter 8 may just write Eei M 1 1 ...

Let 1 , 2 , ... be independent r.v.s having an exponential distribution, and E{

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Let ξ₁, ξ₂, ... be independent r.v.’s having an exponential distribution, and E{ξ_i} = 1. Let S₀ = 0, St = ξ₁ +...+ξ_t, and X_t = C_t exp{−S_t}, where C_t is a constant such that X_t is a martingale.

(a) Find C_t.

(b) Find lim_t→∞ X_t. How fast is such a convergence?

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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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Let 1 , 2 , ... be independent r.v.s having an exponential distribution, and E{

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