Replicating only changes made by a specific database user
I agree with Phil+1 that this is not readily possible.  Furthermore, it is very unclear how this could even work.  Imagine the following simple table is being replicated.

 C1   C2
  1    'Apple'
  2    'Orange'
  3    'Pear'


Scenario 1

 batchjobaccount : INSERT INTO T1 VALUES (4,'Peach');
 appserveraccount: UPDATE T1 SET C2='Grape' WHERE C1=4;


What should happen in the replication?  Should the record be created so that the appserveraccount action can take place or should the update be ignored?

Scenario 2

 batchjobaccount : UPDATE T1 SET C1=5 WHERE C1=2;
 appserveraccount: DELETE FROM T1 WHERE C1=5;


What should happen in the replication?  Should the record be deleted or not?

Scenario 3

 batchjobaccount : DELETE FROM T1 WHERE C1=3;
 appserveraccount: UPDATE T1 SET C2='Strawberry' WHERE C1=3;


What should happen?  Should the update fail on the local database but succeed on the replicated database or should it not run on the remote database because it failed on the local database?

If you don't want changes by batchjobaccount to replicate, then why give them permission to make the changes on the local database?  If they need a local playground, then can you just make a local copy of the tables and only give batchjobaccount access to those?