On SmartOS how to tell if process was killed for OOM

A daemon process of mine gets killed almost immediately, as soon as it starts receiving requests. The application log has absolutely no error output, even when I try to run it in foreground.

I have a suspicion that the OS might be killing it for OOM, because this VM instance has only 512 MB allocated.

I would like to find out what is causing this, but am stymied by the fact that there are very few log files available:

# ls -la /var/log
total 20011

drwxr-xr-x   3 root     sys           10 Oct  9 02:38 .
drwxr-xr-x  31 root     root          31 May 15  2013 ..
-rw-r-----   1 root     root     4914932 Nov 15 16:34 auth.log
-rw-r--r--   1 root     root           0 Sep  9 15:49 courier.log
drwxr-xr-x   3 root     root           5 Nov  8 22:18 httpd
-rw-r--r--   1 root     root     2515768 Sep 10 03:10 postfix.log
-rw-r-----   1 root     other          0 Feb 21  2008 sysidconfig.log
-rw-r-----   1 root     sys      2514934 Sep 10 03:10 syslog
-rw-------   1 root     root         132 Nov  8 18:45 vsftpd.log
-rw-r--r--   1 root     root           0 Jun  5  2012 zoneinit.log

As you can see, syslog is two months old, no new entries have been added lately. And that's all the log files I can find.

I am running on SmartOS:

SunOS hostname 5.11 joyent_20120504T040233Z i86pc i386 i86pc

I have root, of this instance (which in SmartOS parlance is called a "zone", afaik), but do not have control over the whole system.

I've read How do I know if the Linux server killed my process and which process it killed?, but it does not help in my case.