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Computational & Applied Mathematics
On-line version ISSN 1807-0302
WITHERS, Christopher S. and NADARAJAH, Saralees. Solutions to the recurrence relation un+1 = vn+1 + un ⊗ vn in terms of Bell polynomials. Comput. Appl. Math. [online]. 2012, vol.31, n.2, pp.245-258. ISSN 1807-0302. http://dx.doi.org/10.1590/S1807-03022012000200002.
Motivated by time series analysis, we consider the problem of solving the recurrence relation un+1 = vn+1 + un ⊗ vn for n ≠ 0 and un, given the sequence vn. A solution is given as a Bell polynomial. When vn can be written as a weighted sum of nth powers, then the solution un also takes this form. Mathematical subject classification: 33E99.
Keywords : autoregressive processes; Bell polynomials; convolution; maximum.