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Let (W)to be a Brownian Motion. (a) Find an expression with integrals for W4 using Itô formula. (b) Use the result of part (a) to calculate E[W*^]. (c) Repeat parts (a) and (b) to calculate E[W]. (d) Prove by induction that E[W] = (2n)! = t" for all n. n! 2n

Let (W)to be a Brownian Motion. (a) Find an expression with integrals for W4 using Itô formula. (b) Use the result of part (a) to calculate E[W*^]. (c) Repeat parts (a) and (b) to calculate E[W]. (d) Prove by induction that E[W] = (2n)! = t" for all n. n! 2n

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Let (W)to be a Brownian Motion. (a) Find an expression with integrals for W4 using Itô formula. (b) Use the result of part (a) to calculate E[W*^]. (c) Repeat parts (a) and (b) to calculate E[W]. (d) Prove by induction that E[W] = (2n)! = t" for all n. n! 2n
Transcribed Image Text:Let (W)to be a Brownian Motion. (a) Find an expression with integrals for W4 using Itô formula. (b) Use the result of part (a) to calculate E[W*^]. (c) Repeat parts (a) and (b) to calculate E[W]. (d) Prove by induction that E[W] = (2n)! = t" for all n. n! 2n
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