Stochastic chemical kinetics: What's the probability of reaching one state before another?
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Say we've got a system of stochastic chemical reactions, in discrete space and continuous time with specified rates, e.g.
$x_1 rightarrow x_1+1$ with rate $f_1(x_1,x_2)$,
$x_1 rightarrow x_1 -1$ with rate $g_1(x_1,x_2)$,
$x_2 rightarrow x_2 + 1$ with rate $f_1(x_1,x_2)$,
$x_2 rightarrow x_2 -1$ with rate $g_2(x_1,x_2)$.
So e.g. one can run a simulation via the Gillespie algorithm.
What's the probability that $x_1$ will reach some value $lambda_1$ before some other value $lambda_2$?
A specific case: If there is some state $x_1=gamma_1$ at which both $f_1=g_1=0$, it will essentially be "stuck", like an absorbing markov chain. What's the probability of reaching some other state $gamma_2$ before becoming stuck?
(I think that in the single-variable case, this could be equivalent to solving the problem in a countable state space Markov Chain.)
stochastic-processes dynamical-systems monte-carlo chemistry
asked Nov 15 at 18:06
bianca
193
add a comment |
up vote
-1
down vote
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Say we've got a system of stochastic chemical reactions, in discrete space and continuous time with specified rates, e.g.
$x_1 rightarrow x_1+1$ with rate $f_1(x_1,x_2)$,
$x_1 rightarrow x_1 -1$ with rate $g_1(x_1,x_2)$,
$x_2 rightarrow x_2 + 1$ with rate $f_1(x_1,x_2)$,
$x_2 rightarrow x_2 -1$ with rate $g_2(x_1,x_2)$.
So e.g. one can run a simulation via the Gillespie algorithm.
What's the probability that $x_1$ will reach some value $lambda_1$ before some other value $lambda_2$?
A specific case: If there is some state $x_1=gamma_1$ at which both $f_1=g_1=0$, it will essentially be "stuck", like an absorbing markov chain. What's the probability of reaching some other state $gamma_2$ before becoming stuck?
(I think that in the single-variable case, this could be equivalent to solving the problem in a countable state space Markov Chain.)
stochastic-processes dynamical-systems monte-carlo chemistry
asked Nov 15 at 18:06
bianca
193
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Say we've got a system of stochastic chemical reactions, in discrete space and continuous time with specified rates, e.g.
$x_1 rightarrow x_1+1$ with rate $f_1(x_1,x_2)$,
$x_1 rightarrow x_1 -1$ with rate $g_1(x_1,x_2)$,
$x_2 rightarrow x_2 + 1$ with rate $f_1(x_1,x_2)$,
$x_2 rightarrow x_2 -1$ with rate $g_2(x_1,x_2)$.
So e.g. one can run a simulation via the Gillespie algorithm.
What's the probability that $x_1$ will reach some value $lambda_1$ before some other value $lambda_2$?
A specific case: If there is some state $x_1=gamma_1$ at which both $f_1=g_1=0$, it will essentially be "stuck", like an absorbing markov chain. What's the probability of reaching some other state $gamma_2$ before becoming stuck?
(I think that in the single-variable case, this could be equivalent to solving the problem in a countable state space Markov Chain.)
stochastic-processes dynamical-systems monte-carlo chemistry
asked Nov 15 at 18:06
bianca
193
Say we've got a system of stochastic chemical reactions, in discrete space and continuous time with specified rates, e.g.
$x_1 rightarrow x_1+1$ with rate $f_1(x_1,x_2)$,
$x_1 rightarrow x_1 -1$ with rate $g_1(x_1,x_2)$,
$x_2 rightarrow x_2 + 1$ with rate $f_1(x_1,x_2)$,
$x_2 rightarrow x_2 -1$ with rate $g_2(x_1,x_2)$.
So e.g. one can run a simulation via the Gillespie algorithm.
What's the probability that $x_1$ will reach some value $lambda_1$ before some other value $lambda_2$?
A specific case: If there is some state $x_1=gamma_1$ at which both $f_1=g_1=0$, it will essentially be "stuck", like an absorbing markov chain. What's the probability of reaching some other state $gamma_2$ before becoming stuck?
(I think that in the single-variable case, this could be equivalent to solving the problem in a countable state space Markov Chain.)
stochastic-processes dynamical-systems monte-carlo chemistry
stochastic-processes dynamical-systems monte-carlo chemistry
asked Nov 15 at 18:06
bianca
193
asked Nov 15 at 18:06
bianca
193
edited Nov 15 at 18:13
asked Nov 15 at 18:06
bianca
193
asked Nov 15 at 18:06
bianca
193
asked Nov 15 at 18:06
bianca
193
193
add a comment |
add a comment |
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