- #1
Karlisbad
- 130
- 0
If we have the C-K equation in the form (wikipedia
):
[tex] p_{i_3;i_1}(f_3\mid f_1)=\int_{-\infty}^\infty p_{i_3;i_2}(f_3\mid f_2)p_{i_2;i_1}(f_2\mid f_1)df_2 [/tex]
this is the form of some kind of integral equation.. but is there any differential version of it?? (Chapman-Kolmogorov law into a differential form)
By the way i read that you could use a Markov chain (Particle with a finite number of transition states ) to solve by Montecarlo's method the system of equations
[tex] a_{j}+x_{j}=A_{i,j}x_{j} [/tex]
where we must find the x_j and the a_j are known numbers..
the obvious question is..can it be generalized for an infinite number of states to solve Integral equations with K(x,y)=K(y,x):
[tex] f(x)+g(x)=\int_{-\infty}^{\infty}K(x,y)f(x)dx [/tex]
in this last case i was thinking of a process with an infinite number of states, in the 2 cases:
a) the set of infinite states is numerable so [tex] {f1,f2,f3,f4,...} [/tex]
b) the set is Non-numerable.. (you can't label them)..
In these cases i would like to know if there're any applications of MOntecarlos method to solve systems or Integral equations..thanks.
:shy:
[tex] p_{i_3;i_1}(f_3\mid f_1)=\int_{-\infty}^\infty p_{i_3;i_2}(f_3\mid f_2)p_{i_2;i_1}(f_2\mid f_1)df_2 [/tex]
this is the form of some kind of integral equation.. but is there any differential version of it?? (Chapman-Kolmogorov law into a differential form)
By the way i read that you could use a Markov chain (Particle with a finite number of transition states ) to solve by Montecarlo's method the system of equations
[tex] a_{j}+x_{j}=A_{i,j}x_{j} [/tex]
where we must find the x_j and the a_j are known numbers..
the obvious question is..can it be generalized for an infinite number of states to solve Integral equations with K(x,y)=K(y,x):
[tex] f(x)+g(x)=\int_{-\infty}^{\infty}K(x,y)f(x)dx [/tex]
in this last case i was thinking of a process with an infinite number of states, in the 2 cases:
a) the set of infinite states is numerable so [tex] {f1,f2,f3,f4,...} [/tex]
b) the set is Non-numerable.. (you can't label them)..
In these cases i would like to know if there're any applications of MOntecarlos method to solve systems or Integral equations..thanks.
