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Let W denote a standard Brownian motion and define X(t) = µkW (t)– k²t where k € R. Show that X is a martingale and find E(X(t)).

Let W denote a standard Brownian motion and define X(t) = µkW (t)– k²t where k € R. Show that X is a martingale and find E(X(t)).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Let W denote a standard Brownian motion and define X(t) = ekW (t)-k²t where k € R. Show that X is a martingale and find E(X(t)).
Transcribed Image Text:Let W denote a standard Brownian motion and define X(t) = ekW (t)-k²t where k € R. Show that X is a martingale and find E(X(t)).
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