05564764

j

05564764 Medvedev, I.N. Mikhailov, G.A. Recurrent partial averaging in the theory of weighted Monte Carlo methods. Russ. J. Numer. Anal. Math. Model. 24, No. 3, 261-277 (2009). 2009 Walter de Gruyter, Berlin EN Markov chain Monte Carlo method collision integral equation random Neumann series randomized algoritms

doi:10.1515/RJNAMM.2009.016

This paper is a continuation of a series of papers of one or both of the author's, which focus on dealing with the value of collision of the collision integral equation $$\phi(x)^*=\int_Xk(x,x')\phi(x')^*dx'+h(x)$$ by using the Markov chain Monte Carlo method. Let $\{x_n\}$ be a Markov chain breaking with probability one with transition density $p(x,x')$. A random Neumann series is formulated by using the ratio $q(x,x')=\frac{k(x,x')}{p(x,x')}$ and then, through a recurrent representation, a random series $\{\xi_x{}_n{}\}$, of which the expection (if bounded) provides the solution of the collision integral equation. Along this topic, some randomized algoritms with different branching mechanics are also suggested in this paper to achieve the finite variance to ensure the boundness of the expection. Gong Guanglu (Beijing)