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34 views

Ornstein-Uhlenbeck processs: Markov, but not martingale?

I'm puzzled about properties of the Ornstein-Uhlenbeck process, given by the Itō integral $$ X_t = x e^{-\lambda t} + \sigma \int_0^t e^{-\lambda(t-s)} d W_s \,. $$ I compute that $\{X_t\}$ is not ...
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47 views

Is $8^{W(t)}$ a martingale?

I have a standard Wiener process: $W(t)$ I need to determine if the following is a Martingale: $8^{W(t)}$ I know the two conditions for a Martingale; that the expected value of the absolute value ...
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75 views

$X_n/(1+r)^n$ martingale implies $X_n$ not Markov?

If $X_n/(1+r)^n$ is a martingale, I can conclude that $X_n$ is not a martingale. But can I also conclude that $X_n$ is not Markov?