Domain Markov property of a chordal Loewner chain
= Domain Markov property of a chordal Loewner chain
Conditionally on the entire past up to $t$, the future domains mapped and centered by $g_t-U_t$ have the original chain law and are independent of that past. For <Schramm–Loewner evolution> this follows from independent stationary <Brownian motion> increments and the <composition rule for chordal Loewner driving functions>. The <Strong Markov property> gives the version at almost surely finite stopping times.