Use the demo/index.html file in the persistencejs src to answer this question. It has the jquery scripts first and persistencejs second. Here in the order in the demo file:
<script src="http://code.jquery.com/jquery-1.4.4.min.js"></script>
<script src="http://code.jquery.com/mobile/1.0a2/jquery.mobile-1.0a2.min.js"></script>
<script src="http://code.google.com/apis/gears/gears_init.js"></script>
<script src="../../lib/persistence.js"></script>
<script src="../../lib/persistence.store.sql.js"></script>
<script src="../../lib/persistence.store.websql.js"></script>
<script src="../../lib/persistence.store.memory.js"></script>
<script src="../../lib/persistence.jquery.js"></script>
<script src="../../lib/persistence.jquery.mobile.js"></script>
Modify the order to use your own version and last I would loaded your database population script.