Checking members and instantiating in properties

Question

Consider this:

public MyClass
{
    private Resource _myResource;

    public Resource MyResource
    {
        get
        {
            if(_myResource == null)
            {
                _myResource = new Resource();
            }

            return _myResource;
        }
    }

    public void UseResource()
    {
        MyResource.DoSomething();
    }
}

Is this a recognised pattern, or possibly an anti-pattern? I've never seen it suggested in any books, but it does come up time and time again in code I see. I think the logic of this is that _myResource is instantiated 'just in time'. To me, it seems a bit smelly. UserResource() is accessing a public property from within the class, and the resource can never really be accessed through the private member - if someone did, _myResource could be null.

Maybe performance reasons may sometimes necessitate, but I would generally favour instantiating in the constructor, or just having an instance of Resource local to the method.

So is this an accepted pattern, or should it be avoided?