407 2.0 HDI engine leaves sporadic after starting

My Peugeot 407 2.0 HDI Bj. 2005 starts sporadically after starting again. The engine starts, but then it runs unround and then just goes out. If you start a few more start-up attempts then it usually starts again after a few try and then it runs stable and you can drive. During the day it is to be used again and the engine doesn’t go out any more, if it doesn’t run out again. But when the car is standing overnight, the problem occurs more and more often in the morning.With a YouTube video with the phenomenon:http://youtu.be/2BQVFSLa3lc I was already 3 times in a Peugeout factory saddle, but there he always jumped and no error could be read. Once he did not jump at all until the battery, from the start-up attempts, was empty. After that the battery was recharged and tested and there could be no fault of the battery/E On assumption I didn’t want to have any parts replaced, since no one could assure me that the error has been fixed after possible fuel pump replacement. However, some plug connections to the Krafstoffpump have already been changed, but this did not fix the error. Maybe one of you once had a similar problem or has an idea what it could be. Thanks already for any help! Many greetings Christian