Can an amended complaint filed after the statute of limitations be deemed as of the date of the original complaint?

"The relation-back doctrine allows an amendment filed after the statute of limitations has run to be deemed filed as of the date of the original complaint "provided recovery is sought in both pleadings on the same general set of facts." [Citation.] In order for the relation-back doctrine to apply, "the amended complaint must (1) rest on the same general set of facts , (2) involve the same injury , and (3) refer to the same instrumentality , as the original one." [Citation.]" ( Bridgeman v. Allen (2013) 219 Cal.App.4th 288, 296, 161 Cal.Rptr.3d 657.)