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Keywords
(10)
Convergence Rate
Ergodic Theory
Functional Properties
Hitting Time
Markov Process
ornsteinuhlenbeck process
Poincare Inequality
Spectral Gap
Spectral Properties
Tail Probability
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Asymptotic and spectral properties of exponentially \phiergodic Markov processes
Asymptotic and spectral properties of exponentially \phiergodic Markov processes,Alexey M. Kulik
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Asymptotic and spectral properties of exponentially \phiergodic Markov processes
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Citations: 1
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Alexey M. Kulik
New relations between ergodic rate, L_p convergence rates, and asymptotic behavior of tail probabilities for hitting times of a time homogeneous
Markov process
are established. For L_p convergence rates and related spectral and
functional properties
(spectral gap and Poincare inequality) sufficient conditions are given in the terms of an exponential \phicoupling. This provides sufficient conditions for L_p convergence rates in the terms of appropriate combination of `local mixing' and `recurrence' conditions on the initial process, typical in the
ergodic theory
of Markov processes. The range of application of the approach includes timeirreversible processes. In particular, sufficient conditions for
spectral gap
property for Levy driven
OrnsteinUhlenbeck process
are established.
Published in 2009.
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References
(14)
Equivalence of exponential ergodicity and L 2exponential convergence for Markov chains
(
Citations: 17
)
MuFa Chen
Journal:
Stochastic Processes and Their Applications  STOCH PROC APPL
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Subgeometric rates of convergence of fergodic strong Markov processes
(
Citations: 19
)
Randal Douc
,
Gersende Fort
,
Arnaud Guillin
Published in 2006.
a Certain Property of Solutions of Parabolic Equations with Measurable Coefficients
(
Citations: 67
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N. V. Krylov
,
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Journal:
Mathematics of The Ussrizvestiya
, vol. 16, no. 1, pp. 151164, 1981
Absolute Continuity and Convergence in Variation for Distributions of Functionals of Poisson Point Measure
(
Citations: 3
)
Alexey M. Kulik
Journal:
Journal of Theoretical Probability  J THEOR PROBABILITY
, vol. 24, no. 1, pp. 138, 2011
Exponential ergodicity of the solutions to SDE’s with a jump noise
(
Citations: 9
)
Alexey M. Kulik
Journal:
Stochastic Processes and Their Applications  STOCH PROC APPL
, vol. 119, no. 2, pp. 602632, 2009
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Citations
(1)
Exact asymptotic for distribution densities of Levy functionals
Victoria P. Knopova
,
Alexey M. Kulik
Published in 2009.