5.2. A natural candidate for what we could call Brownian motion on the ellipse where a > 0,b >0 %3D is the process X; =(X1(t), X2(t)) defined by X1(t) = a cos B. , X2(t) = bsin B; where B; is 1-dimensional Brownian motion. Show that Xị is a solution of the stochastic differential equation dX = -X,dt + M X¿dB¿ %3D where M =

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stochastic differential equation question

5.2. A natural candidate for what we could call Brownian motion on the
ellipse
{(r, 9);
y?
= 1}
where a > 0,b > 0
a2
is the process Xt = (X1(t), X2(t)) defined by
X1(t) = a cos B, , X2(t) = bsin B;
where Bị is 1-dimensional Brownian motion. Show that X4 is a solution
of the stochastic differential equation
dX; = -}X,dt + M X,dB,
where M =
Transcribed Image Text:5.2. A natural candidate for what we could call Brownian motion on the ellipse {(r, 9); y? = 1} where a > 0,b > 0 a2 is the process Xt = (X1(t), X2(t)) defined by X1(t) = a cos B, , X2(t) = bsin B; where Bị is 1-dimensional Brownian motion. Show that X4 is a solution of the stochastic differential equation dX; = -}X,dt + M X,dB, where M =
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