26
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Limit theorems for monotonic convolution and the Chernoff product formula

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Bercovici and Pata showed that the correspondence between classically, freely, and Boolean infinitely divisible distributions holds on the level of limit theorems. We extend this correspondence also to distributions infinitely divisible with respect to the additive monotone convolution. Because of non-commutativity of this convolution, we use a new technique based on the Chernoff product formula. In fact, the correspondence between the Boolean and monotone limit theorems extends from probability measures to positive measures of total weight at most one. Finally, we study this correspondence for multiplicative monotone convolution, where the Bercovici-Pata bijection no longer holds.

          Related collections

          Author and article information

          Journal
          2012-09-19
          2013-02-19
          Article
          1209.4260
          a4e04147-169c-4591-9bdf-fa2db30443c2

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          46L53 (Primary) 30D05, 46L54, 47D06, 60B10 (Secondary)
          v4: minor corrections. v3: Results extended from probability measures to finite measures. v2: Significant improvements following comments by J.C. Wang; Introduction also modified
          math.OA math.PR

          Probability,Algebra
          Probability, Algebra

          Comments

          Comment on this article