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Problem 1. Solving SDEs: Ornstein-Uhlenbeck process The purpose of this problem is to use Itô lemma to solve the Stochastic Differential Equation with Xo = dX+= (aX+) dt + σ dWt, xo. The solution is known as an Ornstein-Uhlenbeck process. (a) Find an explicit expression for Xt. Hint: use the function f(t, x) Formula. (b) Determine E[X] and Var(X+). (c) Determine lim E[X] and lim Var(X+). 00+7 0047 (d) Is X normally distributed? = etx in Itô

Problem 1. Solving SDEs: Ornstein-Uhlenbeck process The purpose of this problem is to use Itô lemma to solve the Stochastic Differential Equation with Xo = dX+= (aX+) dt + σ dWt, xo. The solution is known as an Ornstein-Uhlenbeck process. (a) Find an explicit expression for Xt. Hint: use the function f(t, x) Formula. (b) Determine E[X] and Var(X+). (c) Determine lim E[X] and lim Var(X+). 00+7 0047 (d) Is X normally distributed? = etx in Itô

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Problem 1. Solving SDEs: Ornstein-Uhlenbeck process The purpose of this problem is to use Itô lemma to solve the Stochastic Differential Equation with Xo = dX+= (aX+) dt + σ dWt, xo. The solution is known as an Ornstein-Uhlenbeck process. (a) Find an explicit expression for Xt. Hint: use the function f(t, x) Formula. (b) Determine E[X] and Var(X+). (c) Determine lim E[X] and lim Var(X+). 00+7 0047 (d) Is X normally distributed? = etx in Itô
Transcribed Image Text:Problem 1. Solving SDEs: Ornstein-Uhlenbeck process The purpose of this problem is to use Itô lemma to solve the Stochastic Differential Equation with Xo = dX+= (aX+) dt + σ dWt, xo. The solution is known as an Ornstein-Uhlenbeck process. (a) Find an explicit expression for Xt. Hint: use the function f(t, x) Formula. (b) Determine E[X] and Var(X+). (c) Determine lim E[X] and lim Var(X+). 00+7 0047 (d) Is X normally distributed? = etx in Itô
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