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Question on Gÿongy' lemma proof



Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?Deterministic interpretation of stochastic differential equationquestion on Leif Andersen's “Interest Rate Modeling, vol 2 Term Structure Models”Ito, Stochastic Exponential and GirsanovDupire's formula proofIs the 'constant weight in the risky asset' portfolio-strategy self-financing?Ito representation unique up to indistinguishability? Proof?Calculating the stochastic integral of $exp(-rt)S_t$Conditional Expectation with Indicator Functions for Poisson Process First Jump Time (Option Pricing PDE)On quadratic covariationDerivation and expectation interchange










1












$begingroup$


I have some questions regarding a proof of Gÿongy's lemma given in 1



I would like to understand the following passage:
$$
int_s=t_0^s=tmathbbEleft[delta(X_s-K)langle dX_srangle^2 right]=
int_s=t_0^s=tmathbbEleft[delta(X_s-K) right] mathbbEleft[langle dX_srangle^2|X_s=K right]
$$



Thanks






stochastic-calculus







share|improve this question









$endgroup$
















    1












    $begingroup$


    I have some questions regarding a proof of Gÿongy's lemma given in 1



    I would like to understand the following passage:
    $$
    int_s=t_0^s=tmathbbEleft[delta(X_s-K)langle dX_srangle^2 right]=
    int_s=t_0^s=tmathbbEleft[delta(X_s-K) right] mathbbEleft[langle dX_srangle^2|X_s=K right]
    $$



    Thanks






    stochastic-calculus







    share|improve this question









    $endgroup$














      1












      1








      1


      1



      $begingroup$


      I have some questions regarding a proof of Gÿongy's lemma given in 1



      I would like to understand the following passage:
      $$
      int_s=t_0^s=tmathbbEleft[delta(X_s-K)langle dX_srangle^2 right]=
      int_s=t_0^s=tmathbbEleft[delta(X_s-K) right] mathbbEleft[langle dX_srangle^2|X_s=K right]
      $$



      Thanks






      stochastic-calculus







      share|improve this question









      $endgroup$




      I have some questions regarding a proof of Gÿongy's lemma given in 1



      I would like to understand the following passage:
      $$
      int_s=t_0^s=tmathbbEleft[delta(X_s-K)langle dX_srangle^2 right]=
      int_s=t_0^s=tmathbbEleft[delta(X_s-K) right] mathbbEleft[langle dX_srangle^2|X_s=K right]
      $$



      Thanks






      stochastic-calculus




      stochastic-calculus






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 2 hours ago









      AguelmameAguelmame

      411




      411




















          1 Answer
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          1












          $begingroup$

          If $X_s neq K $ then the delta function gives zero, and the product is zero. So the term only contributes when $X_s=K$.






          share|improve this answer









          $endgroup$













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            1












            $begingroup$

            If $X_s neq K $ then the delta function gives zero, and the product is zero. So the term only contributes when $X_s=K$.






            share|improve this answer









            $endgroup$

















              1












              $begingroup$

              If $X_s neq K $ then the delta function gives zero, and the product is zero. So the term only contributes when $X_s=K$.






              share|improve this answer









              $endgroup$















                1












                1








                1





                $begingroup$

                If $X_s neq K $ then the delta function gives zero, and the product is zero. So the term only contributes when $X_s=K$.






                share|improve this answer









                $endgroup$



                If $X_s neq K $ then the delta function gives zero, and the product is zero. So the term only contributes when $X_s=K$.







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 43 mins ago









                Magic is in the chainMagic is in the chain

                1,07915




                1,07915



























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