Question: Show that the bounded Jacobi process dt = ( t)dt + q 1 2 t dWt can be obtained by transforming the following mean-reverting process

Show that the bounded Jacobi process dt = ( t)dt + q 1 2 t dWt

can be obtained by transforming the following mean-reverting process

dXt = ( tanh(Xt)) 1 tanh2 (Xt) dt + q 1 tanh2 (Xt) dWt , t 0, X0 = x0,

with t = tanh(Xt), where , and can respectively be expressed with , and .

Furthermore, using the parameter condition 1+ derive the conditions on , and .

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