Prove the Markov property for the stochastic process $Y^x_t=xe^{at+bW_t}$

Given a function $u(t,x)=\mathbb{E}[f(Y^*_t)]$ with $Y^*_0=x$. For $s<t$ we have $\mathbb{E}[f(Y^*_t)]=u(t-s,Y^*_s)$ by the Markov property.

My question is, what should be my $f(Y^*_t)$ to prove the Markov property?

  • $\begingroup$ did you try just the log? $\endgroup$ Jul 12, 2018 at 19:56
  • $\begingroup$ No, actually I just proved the semigroup property, and as a result the process admits the Markov property. $\endgroup$
    – FunnyBuzer
    Jul 16, 2018 at 16:54


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