According to wiki:
http://en.wikipedia.org/wiki/Poisson_process
The probability for the waiting time to observe first arrival in a Poisson process P(T1>t)=exp(-lambda*t)
But what is the Probability Distribution P(T1=t) of the waiting time itself? How to calculate that?
Yes, I know that. But what I mean is in this case, how can one interpret the most probable first passage time where you have a peak at time 0? The point is sometimes, in some systems, the distribution has to very long tail that makes the mean fpt carries less significant meaning in describing...
Hi all,
Suppose I have a kinetic model for a stochastic system of three states, as shown in the attachment. I solve for the probability distribution of the first passage time from A to B and I get the distribution shown on the right hand side.
I can understand that if there is a peak in the...
Ok, I have been stupid about it. Since I have changed one state to absorbing state, the total change of probability for all the states is not zero now, \sum\frac{dP_i}{dt}≠0. Hence the probability vector keeps increasing due to one and only one positive eigenvalue. But it is still strange that...
My system is actually more complicated than a linear markov chain, in the sense that the transition matrix is not tridiagonal. But I think theory still applies. What happened is the transition matrix for original system has all its eigenvalues <0 but by doing the tricks that modifying one of the...
Thanks for your comment. So I try P(t)=P(0)e^{Tt}, where T is the transition matrix with state i being the absorption state, t is the time and P(t) is the probability vector of different states with norm equal 1. I solved the equation in MATLAB numerically and I observed some strange things:
1...
Hi all!
I have a problem on finding the first passage time for kinetic monte carlo model.
Suppose I have a linear kinetic model for n states:
S1<->S2<->S3<->...<->Sn
where all the rate constants k_ij for transition between any two states are known. Is there any general way to find out the...
Maybe I change my question, is there any 'effective' rate constant between A and B in the new system
\frac{dA}{dt} = -a_1A + b_1 C, \\
\frac{dB}{dt} = -b_2 B + a_2 C, \\
\frac{dC}{dt} = a_1 A + b_2 B - (a_2 + b_1) C.
?
Hi everyone,
I have a question on the rate constant of a kinetic model(like the one we use in describing chemical reaction). Suppose we have the following model between two states A and B:
A--(a)-->B
A<--(b)--B
where a, b are the rate constant for the transition. So the corresponding...
Thanks for all the reply. What I mean for Pi in my problem is that if one measure the state of the system at a particular time, there is probability P1 for it being in state 1, and so on. This is the only information I have for the system. I would say Pi is the time average probability of state...
Homework Statement
I have a physical system, which I know the time average statistics. Its probability of being in state 1 is P1, state 2:P2 and state 3:P3. I want to simulate the time behavior of the system.Homework Equations
N/AThe Attempt at a Solution
I assume the rate of transition event...
Actually, what I am trying to do is to change from one parameterization to another and calculate the formula by definition to see if they give the same result under different parameterization, but I am not sure I am doing something valid. For instance, E=\phi_{u}\cdot\phi_{u} where\phi is a...
In differential geometry, how can one show that the area form: √(EG-F2)du\wedgedv is independent of the choice of local parameterization?
Here E,F,G are the coefficients of first fundamental form. Please someone gives me some ideas.
Here I have got a proof of the question, I am not very sure why bother to do it this way, is it because the image of f, f(U), is not necessarily an open set so the inverse may not exist and the method that I posted above doesn't work?
Pf:
f is di ffeomorphic onto its image f(U) means that if...