How can I create a Java 8 LocalDate from a long Epoch time in Milliseconds?

I have an external API that returns me dates as longs, represented as milliseconds since the beginning of the Epoch.

With the old style Java API, I would simply construct a Date from it with

Date myDate = new Date(startDateLong)

What is the equivalent in Java 8’s LocalDate/LocalDateTime classes?

I am interested in converting the point in time represented by the long to a LocalDate in my current local timezone.