Bound on the second derivative of cumulant-generating function

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Let us consider a sub-Gaussian random variable.



We know that its cumulant-generating function is convex. Under which condition do we have that its cumulant-generating function is also semi-concave (i.e., second derivative bounded from above)?




probability convex-analysis laplace-transform cumulants




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    up vote
    0
    down vote

    favorite












    Let us consider a sub-Gaussian random variable.



    We know that its cumulant-generating function is convex. Under which condition do we have that its cumulant-generating function is also semi-concave (i.e., second derivative bounded from above)?




    probability convex-analysis laplace-transform cumulants




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Let us consider a sub-Gaussian random variable.



      We know that its cumulant-generating function is convex. Under which condition do we have that its cumulant-generating function is also semi-concave (i.e., second derivative bounded from above)?




      probability convex-analysis laplace-transform cumulants




      share|cite|improve this question











      Let us consider a sub-Gaussian random variable.



      We know that its cumulant-generating function is convex. Under which condition do we have that its cumulant-generating function is also semi-concave (i.e., second derivative bounded from above)?





      probability convex-analysis laplace-transform cumulants





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 24 at 6:35









      Aristodog

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