The summation of Markov sequences on a finite abelian group
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M. I. Rozhkov
Abstract
We investigate the conditions under which the sum of independent Markov sequences on a finite abelian group G is also a simple homogeneous Markov chain on the group G with some matrix of transition probabilities. The considered problems concern the well-known procedure of consolidation of states of Markov chains. In this paper we develop a method based on the reduction of the initial problem to the solution of a system of special form of nonlinear equations over group algebras. We obtain new conditions under which sums of Markov chains on an arbitrary abelian group G = Zm are Markov chains, and necessary and sufficient conditions under which a sum of independent realisations of the initial Markov chains is also a simple homogeneous Markov chain.
© de Gruyter 2010
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- Identification of a binary Markov chain of order s with r partial connections subjected to additive distortions
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- An estimate of the probability of localisation of the diameter of a random scale-free graph
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- The expressibility problem in a lattice with closure operation
- An algorithm to restore a linear recurring sequence over the ring R = Zpn from a linear complication of its highest coordinate sequence
- The uniform id-decomposition of functions of many-valued logic over homogeneous functions
- The completeness problem in the function algebra of linear integer-coefficient polynomials
- Circuits for disjunction admitting short unitary diagnostic tests
- The group of automorphisms of the set of bent functions
- Complexity of multiplication in commutative group algebras over fields of prime characteristic
- The summation of Markov sequences on a finite abelian group
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Articles in the same Issue
- Bounds for the number of Boolean functions admitting affine approximations of a given accuracy
- Identification of a binary Markov chain of order s with r partial connections subjected to additive distortions
- On conditional Internet graphs whose vertex degrees have no mathematical expectation
- An estimate of the probability of localisation of the diameter of a random scale-free graph
- On a recursive class of plateaued Boolean functions
- On the distribution of some characteristics of a quasimonotone mapping
- The expressibility problem in a lattice with closure operation
- An algorithm to restore a linear recurring sequence over the ring R = Zpn from a linear complication of its highest coordinate sequence
- The uniform id-decomposition of functions of many-valued logic over homogeneous functions
- The completeness problem in the function algebra of linear integer-coefficient polynomials
- Circuits for disjunction admitting short unitary diagnostic tests
- The group of automorphisms of the set of bent functions
- Complexity of multiplication in commutative group algebras over fields of prime characteristic
- The summation of Markov sequences on a finite abelian group
- The asymptotics of the number of repetition-free Boolean functions in the basis B1
