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Let X (t) be a Gaussian process on t€ (0.00) with E(X (t)) = 0 and E(X (t) X (s)) = min (t.s). (a) Show that, for any t. s 20. X (1) X (s)-N (0.t-s). (b) Show that, for any 0≤u

Let X (t) be a Gaussian process on t€ (0.00) with E(X (t)) = 0 and E(X (t) X (s)) = min (t.s). (a) Show that, for any t. s 20. X (1) X (s)-N (0.t-s). (b) Show that, for any 0≤u

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Let X (t) be a Gaussian process on te (0, 0) with E (X (t) = 0 and E (X (t) X (s)) = min (t, s). (a) Show that, for any t, s > 0, X (1) – X (s) - N (0, t– sl). (b) Show that, for any 0<u <s<t, X (t) – X (s) and X (s) - X (u) are independent.
Transcribed Image Text:Let X (t) be a Gaussian process on te (0, 0) with E (X (t) = 0 and E (X (t) X (s)) = min (t, s). (a) Show that, for any t, s > 0, X (1) – X (s) - N (0, t– sl). (b) Show that, for any 0<u <s<t, X (t) – X (s) and X (s) - X (u) are independent.
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