Can I use an EJB in an infinite thread

I would like to know if it's prohibited to use an EJB in an infinite thread(since it can't be given back to the container).

Something like this:

@ManagedBean(eager = true)
@ApplicationScoped
public class TestListenner {

    private ResultThread result;

    @PostConstruct
    public void init() {
        result = new ResultThread ();
        Thread myThread = new Thread(result);
        myThread.start();
    }
    public ResultThread getResult() {
        return result;
    }
}

And the thread:

public class ResultThread implements Runnable{
    @EJB
    private SomeService service;
    private boolean continueWork = true;

    public void run(){
        while(continueWork){
            service.doSomething();
            //some proccessing
        }
    }

I'm working with EJB's since I started working with databases. I went over daofactories and the likes but I forgot about them(it was a year ago). I use them to do actions on my database when an user request a web page on my web app. But now I need to have a thread that calculate things in my database continuously to decrease the response time. If I cannot use EJB for the reason the container needs to have an handle on them, then what should I use ?

Hopefully I can use a class similar to what I'm used to use :

@Stateless
public class SomeServiceImpl implements SomeService {
    @PersistenceContext(unitName = "my-pu")
    private EntityManager em;

    @Override
    public void updateCategory(SomeClass theclass) {
        em.merge(theclass);
    }
}

Edit: The first answer by BalusC in this topic seems to imply that spawning threads in a ManagedBean wouldn't be dangerous in a case where no additional threads could be spawned. Since my bean is ApplicationScoped, which the web-app uses 1 and only 1 instance of it to do background work on the database (I've actually like a TOP 100 "posts" table that needs to be continually recalculated over time so I can query the table -with another bean- to have a fast answer).