The System.Diagnostics assembly is part of the Silverlight CLR framework, but it only includes classes related to debugging, the Process class is not available. Is there any
Using an elevated trust out of browser app (shall we coin ETOOB or OOBET for short) Silverlight 4 application you may be able to start a new app in a new process if it is a COM Automation server. For example:-
dynamic excel = ComAutomationFactory.CreateObject("Excel.Application");
Should fire up Excel in its own procress.