What can we say about the limiting behavior of Xt , as t goes to infinite , where Xt is the solution of the sde $$dX(t) = e^{-t}X(t)dB(t)$$ ?
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You should try. Where is your try. – Behrouz Maleki Jun 27 '16 at 12:00
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Please add your solution – Behrouz Maleki Jun 27 '16 at 12:25
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Well i have tried thats why i'm asking.I have solved the sde and the solution is $$X_t= X_0 \exp\left( \frac14\ ( {{e}^{-2t}-1} ) +\int_{0}^{t}e^{-s}dB_s\right)\quad $$ but i dont know what arguments to use for the limiting behavior of the integral term. – amm Jun 27 '16 at 12:38