The purpose of this problem is to practice the use of Itô formula. We consider the three processes XtW₁ and Y₁ = = t Ꭶ W2 dw, and Z₁ = W₁ = 6tW² + 3t². (a) Using Itô formula, write X as a sum of integrals. - (b) Find an expression for Y which doesn't involve Itô integrals. (c) Prove that (Z) is a martingale using Itô formula. (d) Find Var(Z₁).

The purpose of this problem is to practice the use of Itô formula. We consider the three processes XtW₁ and Y₁ = = t Ꭶ W2 dw, and Z₁ = W₁ = 6tW² + 3t². (a) Using Itô formula, write X as a sum of integrals. - (b) Find an expression for Y which doesn't involve Itô integrals. (c) Prove that (Z) is a martingale using Itô formula. (d) Find Var(Z₁).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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