Good References for Foster Lyapunov Drift Conditions

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I have been reading the paper by Moustakides on the extension of Wald's lemma to Markov processes. The paper uses notation that is followed in Meyn and Tweedie's book on Markov processes and stochastic stability, and ventures into the Foster Lyapunov drift criteria, something that I find a bit difficult to follow.



Can anyone help me with good references that build up material towards these drift conditions in a manner that can be picked up by a grad student having background in measure theoretic probability?




probability markov-process




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    I have been reading the paper by Moustakides on the extension of Wald's lemma to Markov processes. The paper uses notation that is followed in Meyn and Tweedie's book on Markov processes and stochastic stability, and ventures into the Foster Lyapunov drift criteria, something that I find a bit difficult to follow.



    Can anyone help me with good references that build up material towards these drift conditions in a manner that can be picked up by a grad student having background in measure theoretic probability?




    probability markov-process




    share|cite|improve this question





















      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      I have been reading the paper by Moustakides on the extension of Wald's lemma to Markov processes. The paper uses notation that is followed in Meyn and Tweedie's book on Markov processes and stochastic stability, and ventures into the Foster Lyapunov drift criteria, something that I find a bit difficult to follow.



      Can anyone help me with good references that build up material towards these drift conditions in a manner that can be picked up by a grad student having background in measure theoretic probability?




      probability markov-process




      share|cite|improve this question











      I have been reading the paper by Moustakides on the extension of Wald's lemma to Markov processes. The paper uses notation that is followed in Meyn and Tweedie's book on Markov processes and stochastic stability, and ventures into the Foster Lyapunov drift criteria, something that I find a bit difficult to follow.



      Can anyone help me with good references that build up material towards these drift conditions in a manner that can be picked up by a grad student having background in measure theoretic probability?





      probability markov-process





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      asked Jul 23 at 13:46









      Karthik

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          The paper by Jones and Hobert explains "drift" and "minorization" in the context of Markov chains, from the perspective of Markov chain Monte Carlo. Although their main reference is Meyn and Tweedie, they take their time to explain the details, and provide a wonderful set of examples.



          The drift condition they use is slightly different from the usual Foster-Lyapunov drift, but in this Annals of Statistics paper Jones and Hobert (2004), they explain the relationship between the drift conditions, and also study the drift and minorization for a specific example.



          In general, early papers by Jones and a lot of papers by Hobert use drift and minorization, all from the perspective of MCMC. You can also find a lot of work on this by Jeff Rosenthal, specially before 2000s. His perspective is often not limited to MCMC.






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          • Thanks a lot for these references
            – Karthik
            4 hours ago










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          1 Answer
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          active

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          oldest

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          active

          oldest

          votes








          up vote
          1
          down vote













          The paper by Jones and Hobert explains "drift" and "minorization" in the context of Markov chains, from the perspective of Markov chain Monte Carlo. Although their main reference is Meyn and Tweedie, they take their time to explain the details, and provide a wonderful set of examples.



          The drift condition they use is slightly different from the usual Foster-Lyapunov drift, but in this Annals of Statistics paper Jones and Hobert (2004), they explain the relationship between the drift conditions, and also study the drift and minorization for a specific example.



          In general, early papers by Jones and a lot of papers by Hobert use drift and minorization, all from the perspective of MCMC. You can also find a lot of work on this by Jeff Rosenthal, specially before 2000s. His perspective is often not limited to MCMC.






          share|cite|improve this answer





















          • Thanks a lot for these references
            – Karthik
            4 hours ago














          up vote
          1
          down vote













          The paper by Jones and Hobert explains "drift" and "minorization" in the context of Markov chains, from the perspective of Markov chain Monte Carlo. Although their main reference is Meyn and Tweedie, they take their time to explain the details, and provide a wonderful set of examples.



          The drift condition they use is slightly different from the usual Foster-Lyapunov drift, but in this Annals of Statistics paper Jones and Hobert (2004), they explain the relationship between the drift conditions, and also study the drift and minorization for a specific example.



          In general, early papers by Jones and a lot of papers by Hobert use drift and minorization, all from the perspective of MCMC. You can also find a lot of work on this by Jeff Rosenthal, specially before 2000s. His perspective is often not limited to MCMC.






          share|cite|improve this answer





















          • Thanks a lot for these references
            – Karthik
            4 hours ago












          up vote
          1
          down vote










          up vote
          1
          down vote









          The paper by Jones and Hobert explains "drift" and "minorization" in the context of Markov chains, from the perspective of Markov chain Monte Carlo. Although their main reference is Meyn and Tweedie, they take their time to explain the details, and provide a wonderful set of examples.



          The drift condition they use is slightly different from the usual Foster-Lyapunov drift, but in this Annals of Statistics paper Jones and Hobert (2004), they explain the relationship between the drift conditions, and also study the drift and minorization for a specific example.



          In general, early papers by Jones and a lot of papers by Hobert use drift and minorization, all from the perspective of MCMC. You can also find a lot of work on this by Jeff Rosenthal, specially before 2000s. His perspective is often not limited to MCMC.






          share|cite|improve this answer













          The paper by Jones and Hobert explains "drift" and "minorization" in the context of Markov chains, from the perspective of Markov chain Monte Carlo. Although their main reference is Meyn and Tweedie, they take their time to explain the details, and provide a wonderful set of examples.



          The drift condition they use is slightly different from the usual Foster-Lyapunov drift, but in this Annals of Statistics paper Jones and Hobert (2004), they explain the relationship between the drift conditions, and also study the drift and minorization for a specific example.



          In general, early papers by Jones and a lot of papers by Hobert use drift and minorization, all from the perspective of MCMC. You can also find a lot of work on this by Jeff Rosenthal, specially before 2000s. His perspective is often not limited to MCMC.







          share|cite|improve this answer













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          answered 2 days ago









          Greenparker

          203112




          203112











          • Thanks a lot for these references
            – Karthik
            4 hours ago
















          • Thanks a lot for these references
            – Karthik
            4 hours ago















          Thanks a lot for these references
          – Karthik
          4 hours ago




          Thanks a lot for these references
          – Karthik
          4 hours ago












           

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