Question 3 Consider the following deterministic ODE describing the harmonic oscillator problem 3.1 Show that 3.2 Now consider (3) perturbed by noise dX = Ydt, dY == -Xdt. :(X² (t) + Y²(t)) = 0 (x² (t) + (3a) (3b) dX = Ydt dYXdtydW (4a) (4b) where W(t), is a one dimensional Brownian motion. Show using Ito's formula that the following ODE holds for the average energy of the system E(t) = E(X²(t) + Y²(t)) dE(t) dt (5)

Question 3 Consider the following deterministic ODE describing the harmonic oscillator problem 3.1 Show that 3.2 Now consider (3) perturbed by noise dX = Ydt, dY == -Xdt. :(X² (t) + Y²(t)) = 0 (x² (t) + (3a) (3b) dX = Ydt dYXdtydW (4a) (4b) where W(t), is a one dimensional Brownian motion. Show using Ito's formula that the following ODE holds for the average energy of the system E(t) = E(X²(t) + Y²(t)) dE(t) dt (5)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.2: Systems Of Linear Equations In Two Variables

Problem 50E

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