Partial Differential Equations : Wiener Process and Ito's Lemma
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Consider a random variable r satisfying the stochastic differential equation:
Where are positive constants and dX is a Wiener process. Let
(see attached file)
which transforms the domain for r into (-1,1) for Xi Suppose the stochastic equation for the new random variable Xi is in the form:
dXi= a(Xi)dt + b(Xi)dX.
Find the concrete expressions for a(Xi) and b(Xi) and show that a(Xi) and b(Xi) fulfill the conditions:
{a(-1) = 0, and {a(1) = 0,
{b(-1) = 0, and {b(1) = 0.
I am confused because I don't know if you can use Ito's lemma to find the concrete expressions for a(Xi) and b(Xi). Also when taking the partial derivative of ξ with respect to r, I do not know how to treat the absolute value sign. Thanks.
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Wiener Processes and Ito's Lemma are investigated in the following posting. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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