Erratum to: "Ergodicity and exponential β -mixing bound for multidimensional diffusions with jumps" [Stochastic Process. Appl. 117 (2007) 35-56] (DOI:10.1016/j.spa.2006.04.010)

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Abstract

Hiroki Masuda, Graduate School of Mathematics, Kyushu University, presented an erratum on ergodicity and exponential β-mixing bound for multidimensional diffusions with jumps. He clarified that in assumption 2(a), a bounded transition density of Yu△ was supposed to exist, however, X△ was actually needed. In the proof of Lemma 2.4(i) q ∈ (0, 1) from the beginning, although the condition Lemma 2.4(i) contains q possibly lying in [1,2); this point does not affect Lemma 2.4(ii), while the assertion Af(x) ≥ Gf(x) + 0(1) fails. This point is needed to be modified. Moreover, the proof of Lemma 2.5 contains some mistakes in estimating J* f(x): what should be J* f(x).

Original languageEnglish
Pages (from-to)676-678
Number of pages3
JournalStochastic Processes and their Applications
Volume119
Issue number2
DOIs
Publication statusPublished - Feb 1 2009

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Jump Process
Ergodicity
Random processes
Stochastic Processes
Lemma
Transition Density
Assertion
Jump

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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title = "Erratum to: {"}Ergodicity and exponential β -mixing bound for multidimensional diffusions with jumps{"} [Stochastic Process. Appl. 117 (2007) 35-56] (DOI:10.1016/j.spa.2006.04.010)",
abstract = "Hiroki Masuda, Graduate School of Mathematics, Kyushu University, presented an erratum on ergodicity and exponential β-mixing bound for multidimensional diffusions with jumps. He clarified that in assumption 2(a), a bounded transition density of Yu△ was supposed to exist, however, X△ was actually needed. In the proof of Lemma 2.4(i) q ∈ (0, 1) from the beginning, although the condition Lemma 2.4(i) contains q possibly lying in [1,2); this point does not affect Lemma 2.4(ii), while the assertion Af(x) ≥ Gf(x) + 0(1) fails. This point is needed to be modified. Moreover, the proof of Lemma 2.5 contains some mistakes in estimating J* f(x): what should be J* f(x).",
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N2 - Hiroki Masuda, Graduate School of Mathematics, Kyushu University, presented an erratum on ergodicity and exponential β-mixing bound for multidimensional diffusions with jumps. He clarified that in assumption 2(a), a bounded transition density of Yu△ was supposed to exist, however, X△ was actually needed. In the proof of Lemma 2.4(i) q ∈ (0, 1) from the beginning, although the condition Lemma 2.4(i) contains q possibly lying in [1,2); this point does not affect Lemma 2.4(ii), while the assertion Af(x) ≥ Gf(x) + 0(1) fails. This point is needed to be modified. Moreover, the proof of Lemma 2.5 contains some mistakes in estimating J* f(x): what should be J* f(x).

AB - Hiroki Masuda, Graduate School of Mathematics, Kyushu University, presented an erratum on ergodicity and exponential β-mixing bound for multidimensional diffusions with jumps. He clarified that in assumption 2(a), a bounded transition density of Yu△ was supposed to exist, however, X△ was actually needed. In the proof of Lemma 2.4(i) q ∈ (0, 1) from the beginning, although the condition Lemma 2.4(i) contains q possibly lying in [1,2); this point does not affect Lemma 2.4(ii), while the assertion Af(x) ≥ Gf(x) + 0(1) fails. This point is needed to be modified. Moreover, the proof of Lemma 2.5 contains some mistakes in estimating J* f(x): what should be J* f(x).

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