Consider the following stochastic differential equation(SDE) given by dY (t) = (1+Y(t))dt + e'W (t)dW (t) where Y (0) = 0. %3D a. Find Y(t), the solution of the stochastic differential equation. (Hint: You may find it useful to consider d(e-tY (t))] b. Find the mean and variance of Y (t).

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. Consider the following stochastic differential equation(SDE) given by
dY (t) = (1+ Y(t))dt + e'W (t)dW (t)
%3D
where Y (0) = 0.
a. Find Y(t), the solution of the stochastic differential equation.
(Hint: You may find it useful to consider d(e-tY (t))]
b. Find the mean and variance of Y(t).
Transcribed Image Text:. Consider the following stochastic differential equation(SDE) given by dY (t) = (1+ Y(t))dt + e'W (t)dW (t) %3D where Y (0) = 0. a. Find Y(t), the solution of the stochastic differential equation. (Hint: You may find it useful to consider d(e-tY (t))] b. Find the mean and variance of Y(t).
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