How do we do idle time processing in WPF application?

It is the Dispatcher.Hooks.DispatcherInactive event.

A late alternative answer (as a memo to myself):

System.Windows.Interop.ComponentDispatcher.ThreadIdle += (_, __) =>
{
    Debug.Print("Idle");
};

You can dispatch a task (using the Dispatcher in the normal way) with a DispatcherPriority of ApplicationIdle, which will only be executed when the application is idle. Sample code:

DispatcherPriority priority = DispatcherPriority.ApplicationIdle;    
Application.Current.Dispatcher.BeginInvoke(priority, action);