Large deviations for longest runs in Markov chains
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and
Abstract
We continue our investigation on general large deviation principles (LDPs) for longest runs. Previously, a general LDP for the longest success run in a sequence of independent Bernoulli trails was derived in [Z. Liu and X. Yang, A general large deviation principle for longest runs, Statist. Probab. Lett. 110 2016, 128–132]. In the present note, we establish a general LDP for the longest success run in a two-state (success or failure) Markov chain which recovers the previous result in the aforementioned paper. The main new ingredient is to implement suitable estimates of the distribution function of the longest success run recently established in [Z. Liu and X. Yang, On the longest runs in Markov chains, Probab. Math. Statist. 38 2018, 2, 407–428].
Acknowledgements
The authors are grateful to the referee and the editor for several useful comments which lead to a better presentation of the paper.
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Articles in the same Issue
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations
