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Consequently, oo ([/-«*£"» = £9"anm)(^)- (1-76) 71=0 In order to pass from Eq. 74) to Eq. 76, it is necessary to average the series in Eq. , to integrate by the probability measure in the space of trajectories). Such an averaging will be permissible if in Eq. 74) the functions k(x', x). $(x), rj){x) and the quantity q are replaced by their absolute values. The sum of the series will be finite, furthermore, in view of the condition \q\i | < 1. Thus, the finite partial sums of the series of Eq. 16).

35) where k(x, y, A) is replaced with \k(x,y,\)\ while k'(x, y, A) is replaced with |fc'(x,y, A)|. This permits the construction of the majorant mentioned in the condition for weak convergence Eq. 43). 8. Suppose that the inequalities |fc(z,2/, A)| < k0(x,y), \k'(x,y,\)\ kx(x,y) < hold in the interval Ai < A < A2. If A'i, the integral operator with the kernel k\{x, y)/p(x, y), is bounded and the spectral radius of A p ,o, the operator with the kernel kg(x,y)/p(x, y), is less than unity, then condition of Eq.

4). 0 (1-41) 24 Non-analogue Monte Carlo Methods where ip(x, t) = ifi(x + £w), k\(x, y,t) = k{x + tcj, y + tu), hi(x,t) = h(x,tw). This change of variable is convenient in calulations if the original equation is invariant (at least partly) under the translation along the direction o>. 41), the construction of the triangular system of integral equations for the derivatives dni(> dn