For what values of a is this process a well defined Ito integral

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So the question is



For what values of a$in$ $mathbbR$ is the process



$$Y_a(t)=int_0^t(t-s)^adB(s) $$



Well defined as an Ito integral.



By well defined does it mean finite a.s? would it help to look at its expectoration or variance.




probability stochastic-calculus brownian-motion




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    up vote
    0
    down vote

    favorite












    So the question is



    For what values of a$in$ $mathbbR$ is the process



    $$Y_a(t)=int_0^t(t-s)^adB(s) $$



    Well defined as an Ito integral.



    By well defined does it mean finite a.s? would it help to look at its expectoration or variance.




    probability stochastic-calculus brownian-motion




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      So the question is



      For what values of a$in$ $mathbbR$ is the process



      $$Y_a(t)=int_0^t(t-s)^adB(s) $$



      Well defined as an Ito integral.



      By well defined does it mean finite a.s? would it help to look at its expectoration or variance.




      probability stochastic-calculus brownian-motion




      share|cite|improve this question











      So the question is



      For what values of a$in$ $mathbbR$ is the process



      $$Y_a(t)=int_0^t(t-s)^adB(s) $$



      Well defined as an Ito integral.



      By well defined does it mean finite a.s? would it help to look at its expectoration or variance.





      probability stochastic-calculus brownian-motion





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









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