Central Terms of Markov Walks
| Autor: | L. E. Myers |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 1976 |
| Předmět: |
Statistics and Probability
Discrete mathematics Markov kernel Markov chain mixing time Central term Zero (complex analysis) Mathematics::Classical Analysis and ODEs Discrete-time stochastic process Random walk Combinatorics Continuous-time Markov chain 60G17 Bounded function 60J10 60C05 Markov walk 60G25 62M20 Statistics Probability and Uncertainty Invariant (mathematics) Mathematics |
| Zdroj: | Ann. Probab. 4, no. 2 (1976), 313-318 |
| Popis: | A $\{0, 1\}$-valued discrete time stochastic process $\beta = \{\beta_n\}^\infty_{n=1}$ will be referred to simply as a walk. The notion of central (modal) term of a binomial distribution is generalized to the conditional-on-the-past distributions of $N$th partial sums of walks. The emphasis here is placed on the smallest possible central term $V_A(N)$ within a given class $A$ of walks. If $A$ consists of (i) all walks, (ii) all stationary independent walks, (iii) all stationary Markov walks which are invariant under interchange of 0 and 1, then, respectively, (i) $\{N \cdot V_A(N)\}^\infty_{N=1}$, (ii) $\{N^{\frac{1}{2}} \cdot V_A(N)\}^\infty_{N=1}$, (iii) $\{N \cdot V_A(N)/(\log N)^{\frac{1}{2}}\}^\infty_{N=2}$ are bounded sequences which are bounded away from zero. |
| Databáze: | OpenAIRE |
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