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

How do I make a variable always equal to the result of some calculations?

Preparing Indesign booklet with .psd graphics for print

Does it take more energy to get to Venus or to Mars?

Can you replace a racial trait cantrip when leveling up?

What is the result of assigning to std::vector<T>::begin()?

To not tell, not take, and not want

Are there any unintended negative consequences to allowing PCs to gain multiple levels at once in a short milestone-XP game?

Bold, vivid family

In excess I'm lethal

Why don't programming languages automatically manage the synchronous/asynchronous problem?

Is there an analogue of projective spaces for proper schemes?

Which tube will fit a -(700 x 25c) wheel?

What is "(CFMCC)" on an ILS approach chart?

Received an invoice from my ex-employer billing me for training; how to handle?

If the heap is initialized for security, then why is the stack uninitialized?

Several mode to write the symbol of a vector

Won the lottery - how do I keep the money?

Unreliable Magic - Is it worth it?

Is it professional to write unrelated content in an almost-empty email?

What connection does MS Office have to Netscape Navigator?

Would a completely good Muggle be able to use a wand?

How to invert MapIndexed on a ragged structure? How to construct a tree from rules?

How to safely derail a train during transit?

Would this house-rule that treats advantage as a +1 to the roll instead (and disadvantage as -1) and allows them to stack be balanced?



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




















          0






          active

          oldest

          votes












          Your Answer





          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader:
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          ,
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













          draft saved

          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3153292%2freverse-hoeffding-inequalities%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes















          draft saved

          draft discarded
















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid


          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.

          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3153292%2freverse-hoeffding-inequalities%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          Moe incest case Sentencing See also References Navigation menu"'Australian Josef Fritzl' fathered four children by daughter""Small town recoils in horror at 'Australian Fritzl' incest case""Victorian rape allegations echo Fritzl case - Just In (Australian Broadcasting Corporation)""Incest father jailed for 22 years""'Australian Fritzl' sentenced to 22 years in prison for abusing daughter for three decades""RSJ v The Queen"

          John Burke, 9th Earl of Clanricarde References Navigation menuA General and heraldic dictionary of the peerage and baronetage of the British EmpireLeigh Rayment's Peerage Pages

          Sum infinite sum for a complex variable not in the integers The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Convergence of the infinite product $prod_n = 1^infty fracz - alpha_nz - beta_n$Suppose $sum_k=-infty^inftya_kz^k$ and $sum_-infty^inftyb_kz^k$ converge to $1/sin(pi z)$. Find $b_k-a_k$.Laurent series of $ 1over (z - i) $Laurent series for $z^2 e^1/z$ at $z = infty$Write $sumlimits_n=0^infty e^-xn^3$ in the form $sumlimits_n=-infty^infty a_nx^n$Help needed on laurent series for a complex functionShow that $sum_-infty^infty (-1)^nexp(nz-frac12(n+frac12)^2omega)$ converges and is entireΑn entire function as an infinite sum of entire functionsClassify singularities in the extended complex planeFinding the laurent series around z = 0