# Prove the Markov property for the stochastic process $Y^x_t$

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?

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