Construction of a stochastic process

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I would appreciate some help constructing a stochastic process. Specifically an ASEP.



I want the process $eta_t$ to take values in $0,1$$^(-infty,m]$. And I want there to always be k particles (i.e k 1's) so $sum_j=-infty^m(eta_t)_j=k$



Defining $zin$$0,1$$^(-infty,m]$ and



$(z^i , j)_l =$



$ z_l $ if $l$ $neq i,j $



$ z_l-1 $ if $l$ $=i$



$ z_l+1 $ if $l$ $=j$



I.e describing a shift. Then I want the process to be in a distribution such that
$$P(eta=z)=(q/p)P(eta=z^i,i+1) $$



Where $p>1/2$ $p+q=1$ Im basically asking what process has rates which will make the above work.




stochastic-processes markov-process




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  • By ASEP do you mean "asymmetric simple exclusion process"?
    – Math1000
    Jul 24 at 2:27














up vote
0
down vote

favorite












I would appreciate some help constructing a stochastic process. Specifically an ASEP.



I want the process $eta_t$ to take values in $0,1$$^(-infty,m]$. And I want there to always be k particles (i.e k 1's) so $sum_j=-infty^m(eta_t)_j=k$



Defining $zin$$0,1$$^(-infty,m]$ and



$(z^i , j)_l =$



$ z_l $ if $l$ $neq i,j $



$ z_l-1 $ if $l$ $=i$



$ z_l+1 $ if $l$ $=j$



I.e describing a shift. Then I want the process to be in a distribution such that
$$P(eta=z)=(q/p)P(eta=z^i,i+1) $$



Where $p>1/2$ $p+q=1$ Im basically asking what process has rates which will make the above work.




stochastic-processes markov-process




share|cite|improve this question



















  • By ASEP do you mean "asymmetric simple exclusion process"?
    – Math1000
    Jul 24 at 2:27












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I would appreciate some help constructing a stochastic process. Specifically an ASEP.



I want the process $eta_t$ to take values in $0,1$$^(-infty,m]$. And I want there to always be k particles (i.e k 1's) so $sum_j=-infty^m(eta_t)_j=k$



Defining $zin$$0,1$$^(-infty,m]$ and



$(z^i , j)_l =$



$ z_l $ if $l$ $neq i,j $



$ z_l-1 $ if $l$ $=i$



$ z_l+1 $ if $l$ $=j$



I.e describing a shift. Then I want the process to be in a distribution such that
$$P(eta=z)=(q/p)P(eta=z^i,i+1) $$



Where $p>1/2$ $p+q=1$ Im basically asking what process has rates which will make the above work.




stochastic-processes markov-process




share|cite|improve this question











I would appreciate some help constructing a stochastic process. Specifically an ASEP.



I want the process $eta_t$ to take values in $0,1$$^(-infty,m]$. And I want there to always be k particles (i.e k 1's) so $sum_j=-infty^m(eta_t)_j=k$



Defining $zin$$0,1$$^(-infty,m]$ and



$(z^i , j)_l =$



$ z_l $ if $l$ $neq i,j $



$ z_l-1 $ if $l$ $=i$



$ z_l+1 $ if $l$ $=j$



I.e describing a shift. Then I want the process to be in a distribution such that
$$P(eta=z)=(q/p)P(eta=z^i,i+1) $$



Where $p>1/2$ $p+q=1$ Im basically asking what process has rates which will make the above work.





stochastic-processes markov-process





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 19 at 16:53









Monty

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  • By ASEP do you mean "asymmetric simple exclusion process"?
    – Math1000
    Jul 24 at 2:27
















  • By ASEP do you mean "asymmetric simple exclusion process"?
    – Math1000
    Jul 24 at 2:27















By ASEP do you mean "asymmetric simple exclusion process"?
– Math1000
Jul 24 at 2:27




By ASEP do you mean "asymmetric simple exclusion process"?
– Math1000
Jul 24 at 2:27















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