Stochastic chemical kinetics: What's the probability of reaching one state before another?
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
add a comment |
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
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
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
edited Nov 15 at 18:13
asked Nov 15 at 18:06
bianca
193
193
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3000044%2fstochastic-chemical-kinetics-whats-the-probability-of-reaching-one-state-befor%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown