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$begingroup$

I was working on a stochastic model and the following question arouse:

Let $X_t = B_t$, where $B$ is the standard bronian motion.

Also, let $H_a = inf lbrace t: X_t = a rbrace$.

Then, what is $mathbbEleft[X|H_a,X_0=b right]$?

I haven't find the joint density $f(X,H_a)$. Anyone has any guess?

probability-theory brownian-motion stopping-times

share|cite|improve this question

asked yesterday

Nicolas Pimentel de SouzaNicolas Pimentel de Souza

85

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, is $X$ standard BM or not?
  $endgroup$
  – Will M.
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes it is the standard BM
  $endgroup$
  – Nicolas Pimentel de Souza
  yesterday
  

  
  
  
  

add a comment | 

0

1

$begingroup$

I was working on a stochastic model and the following question arouse:

Let $X_t = B_t$, where $B$ is the standard bronian motion.

Also, let $H_a = inf lbrace t: X_t = a rbrace$.

Then, what is $mathbbEleft[X|H_a,X_0=b right]$?

I haven't find the joint density $f(X,H_a)$. Anyone has any guess?

probability-theory brownian-motion stopping-times

share|cite|improve this question

asked yesterday

Nicolas Pimentel de SouzaNicolas Pimentel de Souza

85

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, is $X$ standard BM or not?
  $endgroup$
  – Will M.
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes it is the standard BM
  $endgroup$
  – Nicolas Pimentel de Souza
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

I was working on a stochastic model and the following question arouse:

Let $X_t = B_t$, where $B$ is the standard bronian motion.

Also, let $H_a = inf lbrace t: X_t = a rbrace$.

Then, what is $mathbbEleft[X|H_a,X_0=b right]$?

I haven't find the joint density $f(X,H_a)$. Anyone has any guess?

probability-theory brownian-motion stopping-times

share|cite|improve this question

asked yesterday

Nicolas Pimentel de SouzaNicolas Pimentel de Souza

85

$endgroup$

share|cite|improve this question

asked yesterday

Nicolas Pimentel de SouzaNicolas Pimentel de Souza

85

share|cite|improve this question

asked yesterday

Nicolas Pimentel de SouzaNicolas Pimentel de Souza

85

asked yesterday

Nicolas Pimentel de SouzaNicolas Pimentel de Souza

85

asked yesterday

Nicolas Pimentel de SouzaNicolas Pimentel de Souza

85