Let (W)to be a Brownian Motion. (a) Let Xt, check that (X+) is an Itô-integrable process. (b) Let Y₁ = sdWs. Find E[Y] and Var(Y). (c) Let Z= W, ds (note that this is a Riemann integral, Using approximation by simple processes or Itô formula, prove that In other words, prove that Yt+Zt=tWt. I saw. + [W₁ds = W₁. L sdWs =tWt. This should remind you of the formula for the derivative of a product or the inte- gration by parts formula.
Let (W)to be a Brownian Motion. (a) Let Xt, check that (X+) is an Itô-integrable process. (b) Let Y₁ = sdWs. Find E[Y] and Var(Y). (c) Let Z= W, ds (note that this is a Riemann integral, Using approximation by simple processes or Itô formula, prove that In other words, prove that Yt+Zt=tWt. I saw. + [W₁ds = W₁. L sdWs =tWt. This should remind you of the formula for the derivative of a product or the inte- gration by parts formula.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
Question
![Let (W)to be a Brownian Motion.
(a) Let Xt, check that (X+) is an Itô-integrable process.
(b) Let Y₁ =
sdWs. Find E[Y] and Var(Y).
(c) Let Z=
W, ds (note that this is a Riemann integral,
Using approximation by simple processes or Itô formula, prove that
In other words, prove that
Yt+Zt=tWt.
I saw. + [W₁ds = W₁.
L
sdWs
=tWt.
This should remind you of the formula for the derivative of a product or the inte-
gration by parts formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a1c925e-790f-448e-9276-e5adcf0e8758%2F219afa02-7bab-4c1c-8cc8-cc1dbd8b2ea4%2Fwce7sit_processed.png&w=3840&q=75)
Transcribed Image Text:Let (W)to be a Brownian Motion.
(a) Let Xt, check that (X+) is an Itô-integrable process.
(b) Let Y₁ =
sdWs. Find E[Y] and Var(Y).
(c) Let Z=
W, ds (note that this is a Riemann integral,
Using approximation by simple processes or Itô formula, prove that
In other words, prove that
Yt+Zt=tWt.
I saw. + [W₁ds = W₁.
L
sdWs
=tWt.
This should remind you of the formula for the derivative of a product or the inte-
gration by parts formula.
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