<p>Is it possible to call a stored procedure from another stored procedure asynchronously?</p>

<p><strong>Edit:</strong> Specifically I'm working with a DB2 database.
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Executive summary:  Yes, if your database has a message queue service.
You can push a message onto a queue and the queue processor will consume it asynchronously.
Oracle: queues
Sql Server: service broker
DB2: event broker
For "pure" stored procedure languages (PL/Sql or T-Sql) the answer is no, since it works against the fundamental transaction model most databases have.
However, if your database has a queuing mechanism, you can use that to get the same result.