- #1

Karlisbad

- 131

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[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: