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Reverse Hoeffding Inequalities



The Next CEO of Stack OverflowIs there a discrete-time analogue of Doléans-Dade exponential?Generalization of Hoeffding InequalityOptimal Stopping TheoremAzuma inequality with probabilistic bound for the incrementsDoob's inequalities for not necessarily right-continuous martingalesHoeffding Inequality.Generalizing Doob's super-martingale inequalityApplication of Hoeffding inequalityHow to get the following upper and lower bounds of $E[sup_ngeq 0 M_n]$?A 'reverse' Hoeffding Inequality










0












$begingroup$


Suppose that $X_t$ is a super-martingale, the Hoeffding inquality gives an exponential upper bound on the quatity
$$
mathbbPleft(
sup_0 leq tleq TX_t
geq x
right).
$$



When can a lower-bound be obtained; that is a function of $x$ and $t$ such that
$$
f(t,x)leq mathbbPleft(
sup_0 leq tleq T X_t
geq x
right)?
$$










share|cite|improve this question









$endgroup$
















    0












    $begingroup$


    Suppose that $X_t$ is a super-martingale, the Hoeffding inquality gives an exponential upper bound on the quatity
    $$
    mathbbPleft(
    sup_0 leq tleq TX_t
    geq x
    right).
    $$



    When can a lower-bound be obtained; that is a function of $x$ and $t$ such that
    $$
    f(t,x)leq mathbbPleft(
    sup_0 leq tleq T X_t
    geq x
    right)?
    $$










    share|cite|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      Suppose that $X_t$ is a super-martingale, the Hoeffding inquality gives an exponential upper bound on the quatity
      $$
      mathbbPleft(
      sup_0 leq tleq TX_t
      geq x
      right).
      $$



      When can a lower-bound be obtained; that is a function of $x$ and $t$ such that
      $$
      f(t,x)leq mathbbPleft(
      sup_0 leq tleq T X_t
      geq x
      right)?
      $$










      share|cite|improve this question









      $endgroup$




      Suppose that $X_t$ is a super-martingale, the Hoeffding inquality gives an exponential upper bound on the quatity
      $$
      mathbbPleft(
      sup_0 leq tleq TX_t
      geq x
      right).
      $$



      When can a lower-bound be obtained; that is a function of $x$ and $t$ such that
      $$
      f(t,x)leq mathbbPleft(
      sup_0 leq tleq T X_t
      geq x
      right)?
      $$







      probability probability-theory large-deviation-theory extreme-value-theorem






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 18 at 20:43









      AIM_BLBAIM_BLB

      2,5342820




      2,5342820




















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