PL/SQL :: Same Value Until Field Changes

I have bills and payments for a customer, a customer may make many payments against 1 bill. I want to figure out the time taken from bill issue date to the time the balance of the customer falls to less then 10% of the most recent bill.I have managed to compute the running balance for the customer

So something like:
DATE      AMT      BILL_AMT     BILL_DATE     BALANCE
6-Oct-11     38533 38533     6-Oct-11 38533
20-Sep-12     -6000           0
6-Dec-11     78552 78552     6-Dec-11 78552
[code]....

But I need to know when the running balance falls beneath 10% of the previous bill.

I thought a way to do this would be to keep the same bill amount in the BILL_AMT column until the BILL_AMT is not null which means that a new bill has been issued.

I can't use LAG because the number of records I am going back by increases by 1 for each row where the BILL_AMT is null.I also can't use a running total because I don't want the total for all of the records for the customer, just the total (i.e. the bill amount and all intervening nulls (which would be the bill amount)) since the last bill?

i.e. how can I keep the same value in a field as long as the values in that field are null and then adopt a new value when there is a non-null value?