On an algorithm for calculating the potential of a simple random walk on a cubic lattice. (Russian) Zbl 0738.65105

Kabanovich, V. I.; Kurbatov, A. M.

Zh. Vychisl. Mat. Mat. Fiz. 31, No. 10, 1596-1598 (1991).

The authors construct an algorithm for the computation of the potential of a simple random walk on a three-dimensional cubic lattice. The potential is defined as \[ G(l,m,n)={3\over 8\pi^ 3}\int^{2\pi}_ 0\int^{2\pi}_ 0\int^{2\pi}_ 0{\cos(l\varphi+m\psi+n\theta)d \varphi d\psi d\theta\over 3-\cos \varphi-\cos \psi-\cos \theta}. \] The evaluation of \(k\) decimal points of \(G\) by means of the proposed algorithm is of the same complexity as the multiplication of \(k\)-digit numbers.

Reviewer: I.S.Molchanov (Kiev)

MSC:

65C99	Probabilistic methods, stochastic differential equations
65D32	Numerical quadrature and cubature formulas
65Y20	Complexity and performance of numerical algorithms
60G50	Sums of independent random variables; random walks

Keywords:

computational complexity; numerical integration; algorithm; potential; random walk; cubic lattice