Before revision:  In this article, when X is transient under the objective measure, we investigate what information is necessary and sufficient to recover . We also introduce the notion of a reference function, which contains the information near the area where the process X lies with high probability under the objective measure. A reference function will be used for empirical purposes when X is transient under the objective measure .
After revision:  In this article, when X is transient under the objective measure, we investigate what information is necessary and sufficient to recover .