The paper is organized as follows: (1) A probabilistic part. We introduce multivariate residual lifetimes and discuss different ways of investigating their asymptotic behavior. We briefly go into the relation with multivariate record sequences. We introduce the concepts of stability and strict stability. (2) An algebraic part. Our problem: to describe the possible connected subgroups of the group of coordinate affine transformations on Rd. We give a brief introduction to Lie algebras based on Z. J. Jurek and J. D. Mason. This enables us to give a complete answer to the problem. (3) The description of the strictly multivariate residual lifetime distributions.
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