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Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t ≤ R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims o E [X(0)(X(t+8) − X(t))] = 0 for all t. Use the Schwarz inequality.

Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t ≤ R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims o E [X(0)(X(t+8) − X(t))] = 0 for all t. Use the Schwarz inequality.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t e R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims→0 E[X(0)(X(t+8) – X(t))] = 0 for all t. Use the Schwarz inequality.
Transcribed Image Text:Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t e R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims→0 E[X(0)(X(t+8) – X(t))] = 0 for all t. Use the Schwarz inequality.
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