Titlebook: Markov Processes for Stochastic Modeling; Masaaki Kijima Book 1997 M. Kijima 1997 Markov chain.Markov process.Parameter.algebra.modeling

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bizarre

Discrete-time Markov chains,This chapter concerns discrete-time Markov chains defined on a finite or denumerably infinite state space .. The Markov chains under consideration are assumed to be homogeneous. We assume without loss of generality that the state space consists of nonnegative integers . = ?0,1,...,.”, where . < ∞ or . = ∞.

mechanism

招待

Review of matrix theory,In this section we discuss nonnegative matrices . = (..), i.e., .. ≥ 0 for all ., in which case we write . ≥ O. If .. > 0 for all ., we write . > O. For two matrices . and ., we write . ≥ . if and only if . ≥ O and . > . if and only if . ? . > O. Throughout this section, we assume that matrices are finite and square.

博愛家

https://doi.org/10.1007/978-1-4899-3132-0Markov chain; Markov process; Parameter; algebra; modeling

CRP743

cunning

Total positivity,ere are indeed only ‘the tip of the iceberg’. The reader interested in a complete discussion of the theory of total positivity should consult Karlin (1968). Throughout this appendix, ., . and . represent either intervals of the real line . ≡ (?∞, ∞) or a countable or finite set of discrete values along ..

Mingle

Introduction,or ‘chance’. Markov processes are a class of stochastic processes that are distinguished by the Markov property and have many applications in, for example, operations research, biology, engineering, and economics. In this chapter, we introduce some basic concepts of Markov processes.

枕墊

Monotone Markov chains,n matrices. A Markov chain {.. }is said to be increasing (decreasing, respectively) if .. ? .. (.. ? ..) for all n = 0,1, ..., where ? denotes an ordering relation in some stochastic sense, and in either case we call {.. }., or monotone for short. An . is such that, for two Markov chains {.. }and {.

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