Paper Citation Record · LEDGER

Multi-time Markov renewal chains and stratified renewal theorems

As of 18 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2607.07283.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.07283 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-09T16:09:53.719855Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact27
verified fuzzy3
unresolved0
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malformed identifier0
metadata mismatch6

External citation measurements

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Outbound references

Observation 76d5421c-da6f-4356-87ec-0081e3145963 · outbound

This paper cites On the Markov Renewal Theorem.Stochastic Processes and their Applications 50(1)37–56.

Multi-time Markov renewal chains and stratified renewal theorems On the Markov Renewal Theorem.Stochastic Processes and their Applications 50(1)37–56

Reference 1

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.049402Z

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Observation 861411ef-a488-4b5f-834e-c2a8a79861ed · outbound

This paper cites Stopping Times and Tightness.

Multi-time Markov renewal chains and stratified renewal theorems Stopping Times and Tightness

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-07-09T16:16:20.066109Z

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Observation 0f841a5b-0a5b-48e3-be56-eb3883bb05a1 · outbound

This paper cites S.andLimnios, N.(2008).Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA Analysis.Lecture Notes in Statistics191.

Multi-time Markov renewal chains and stratified renewal theorems S.andLimnios, N.(2008).Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA Analysis.Lecture Notes in Statistics191

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T16:16:20.137104Z

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Observation 7b03704e-02d1-4fe1-8852-09255d6e88e9 · outbound

This paper cites doi: 10.1007/978-0-387-73173-5.

Multi-time Markov renewal chains and stratified renewal theorems doi: 10.1007/978-0-387-73173-5

Reference 4

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.009087Z

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Observation 679b75ee-1bcb-440a-a095-b5e4a3e508f8 · outbound

This paper cites Billingsley,Convergence of Probability Measures.

Multi-time Markov renewal chains and stratified renewal theorems Billingsley,Convergence of Probability Measures

Reference 5

Resolution: metadata mismatch; doi, observed 2026-07-09T16:16:20.041509Z

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Observation 2ed3c046-8b85-4abe-8b5e-4e724fc90c94 · outbound

This paper cites B.(1975).

Multi-time Markov renewal chains and stratified renewal theorems B.(1975)

Reference 6

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.083428Z

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Observation 58895633-1d47-4b34-b509-a8f3f633aec9 · outbound

This paper cites IEEE Transactions on Information Theory 25(5):601–604.

Multi-time Markov renewal chains and stratified renewal theorems IEEE Transactions on Information Theory 25(5):601–604

Reference 7

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.062958Z

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Observation 514627d8-e947-42b7-9805-c93e390b5af6 · outbound

This paper cites Springer, Cham.

Multi-time Markov renewal chains and stratified renewal theorems Springer, Cham

Reference 8

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.077437Z

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Observation 2301e18d-c66a-4961-ba0d-ab95a5e60f67 · outbound

This paper cites Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks.The Annals of Applied Probability14(3)1202–1241.

Multi-time Markov renewal chains and stratified renewal theorems Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks.The Annals of Applied Probability14(3)1202–1241

Reference 9

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.052105Z

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Observation becf613d-6da8-4aab-98c6-83888acf9b0a · outbound

This paper cites L.(2001).

Multi-time Markov renewal chains and stratified renewal theorems L.(2001)

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-09T16:16:20.058017Z

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Observation 215fb109-25a4-47e4-bb72-8d64b27333fc · outbound

This paper cites Springer, Berlin.

Multi-time Markov renewal chains and stratified renewal theorems Springer, Berlin

Reference 11

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.068265Z

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Observation bec8b679-c57d-4845-b7e4-208277e33625 · outbound

This paper cites J.(1974a).

Multi-time Markov renewal chains and stratified renewal theorems J.(1974a)

Reference 12

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.075773Z

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Observation f9640eb6-ab66-49f3-bcbc-a7ebcf1df141 · outbound

This paper cites J.(1974b).

Multi-time Markov renewal chains and stratified renewal theorems J.(1974b)

Reference 13

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.011448Z

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Observation 736beebc-7c09-41d2-b880-bd10a469f7bd · outbound

This paper cites Foundations of Modern Probability , year =.

Multi-time Markov renewal chains and stratified renewal theorems Foundations of Modern Probability , year =

Reference 14

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.067045Z

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Observation db9412cb-fde6-45b6-9823-45b33ae1a817 · outbound

This paper cites Stability of the spectrum for transfer operators.Annali della Scuola Normale Superiore di Pisa.

Multi-time Markov renewal chains and stratified renewal theorems Stability of the spectrum for transfer operators.Annali della Scuola Normale Superiore di Pisa

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T16:16:20.132455Z

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Observation 634dd592-3329-4b05-84bb-38d1417365b9 · outbound

This paper cites Freedman, Another note on the borel-cantelli lemma and the strong law, with the poisson approxi- mation as a by-product, Annals of Probability 1 (6) (1973) 910–925.

Multi-time Markov renewal chains and stratified renewal theorems Freedman, Another note on the borel-cantelli lemma and the strong law, with the poisson approxi- mation as a by-product, Annals of Probability 1 (6) (1973) 910–925

Reference 16

Resolution: metadata mismatch; arxiv_id, observed 2026-07-09T16:16:20.055149Z

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Observation 4b88cecc-f8f6-4e99-b1a0-0b693d388a30 · outbound

This paper cites Springer.

Multi-time Markov renewal chains and stratified renewal theorems Springer

Reference 17

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.059121Z

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Observation 7b9809a6-5294-4627-b9d7-a43d887a4baf · outbound

This paper cites I.(1991).

Multi-time Markov renewal chains and stratified renewal theorems I.(1991)

Reference 18

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.030702Z

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Observation ead0cb88-345d-4d08-b9b5-81555d12aeb4 · outbound

This paper cites Time multidimensional Markov Renewal chains -- An algebraic approach.

Multi-time Markov renewal chains and stratified renewal theorems Time multidimensional Markov Renewal chains -- An algebraic approach

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-07-09T16:16:20.081200Z

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Observation ba7d7f98-1f62-422f-a248-b43459c48c1e · outbound

This paper cites Discrete time-multidimensional renewal theory and applications.

Multi-time Markov renewal chains and stratified renewal theorems Discrete time-multidimensional renewal theory and applications

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-07-09T16:16:20.044453Z

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Observation 31b62eca-1219-45c2-8d71-c3119f2f1582 · outbound

This paper cites Algebraic and FFT-Based Methods for Discrete-Time Matrix Convolutions with Applications to Semi-Markov Models.

Multi-time Markov renewal chains and stratified renewal theorems Algebraic and FFT-Based Methods for Discrete-Time Matrix Convolutions with Applications to Semi-Markov Models

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-07-09T16:16:20.069809Z

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Observation d8f6378c-5ddf-4f74-b2a0-be6236656666 · outbound

This paper cites Birkh¨ auser, Boston.

Multi-time Markov renewal chains and stratified renewal theorems Birkh¨ auser, Boston

Reference 22

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.083213Z

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Observation 746bf751-6d00-4986-8565-f22a671b1d40 · outbound

This paper cites Some Renewal Theorems for Random Walks in Multidimensional Time.Mathematical Proceedings of the Cambridge Philosophical Society95(1)149–154.

Multi-time Markov renewal chains and stratified renewal theorems Some Renewal Theorems for Random Walks in Multidimensional Time.Mathematical Proceedings of the Cambridge Philosophical Society95(1)149–154

Reference 23

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.045275Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f5d1b561-a139-4fbf-9c2d-2ed7b4a43049 · outbound

This paper cites Multivariate Geometric Distributions, (Logarithmically) Monotone Sequences, and Infinitely Divisible Laws.Journal of Multivariate Analysis115(C)457–480.

Multi-time Markov renewal chains and stratified renewal theorems Multivariate Geometric Distributions, (Logarithmically) Monotone Sequences, and Infinitely Divisible Laws.Journal of Multivariate Analysis115(C)457–480

Reference 24

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.073453Z

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Observation 0dacc9ea-8872-49f5-915e-4ad3afcbaca4 · outbound

This paper cites and Ycart, B.

Multi-time Markov renewal chains and stratified renewal theorems and Ycart, B

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-07-09T16:16:20.007015Z

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Observation 26e28109-f3f0-4bb2-a9b7-b4b863c28d6c · outbound

This paper cites 2012.Markov chains and stochastic stability.

Multi-time Markov renewal chains and stratified renewal theorems 2012.Markov chains and stochastic stability

Reference 26

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.057090Z

Source-reported events for the cited work

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Observation 8fe7ed52-8e71-4c55-aa07-e730c3aab0e6 · outbound

This paper cites Hitting Probabilities in a Markov Additive Process with Linear Movements and Upward Jumps.The Annals of Applied Probability14(2)1029–1054.

Multi-time Markov renewal chains and stratified renewal theorems Hitting Probabilities in a Markov Additive Process with Linear Movements and Upward Jumps.The Annals of Applied Probability14(2)1029–1054

Reference 27

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.046360Z

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Observation 1d809033-64e7-4179-8a58-2c2534b33c75 · outbound

This paper cites an unresolved cited work.

Multi-time Markov renewal chains and stratified renewal theorems Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.061020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0b310169-0c4c-4ce3-af3e-b9b7052c85db · outbound

This paper cites The Renewal Theorem for Random Walk in Two-Dimensional Time.Studia Mathematica44(1)71–85.

Multi-time Markov renewal chains and stratified renewal theorems The Renewal Theorem for Random Walk in Two-Dimensional Time.Studia Mathematica44(1)71–85

Reference 29

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.064913Z

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Observation a9bbcdfb-5602-4946-839c-15e8cb525aec · outbound

This paper cites Uniform and Ratio Limit Theorems for Markov Renewal and Semi- Regenerative Processes on a General State Space.Annales de l’Institut Henri Poincar´ e, Section B 14(2)119–143.

Multi-time Markov renewal chains and stratified renewal theorems Uniform and Ratio Limit Theorems for Markov Renewal and Semi- Regenerative Processes on a General State Space.Annales de l’Institut Henri Poincar´ e, Section B 14(2)119–143

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T16:16:20.137540Z

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Observation 7f4f793c-dcbe-48b5-bf7c-59bcaa283184 · outbound

This paper cites Cambridge Tracts in Mathematics83.

Multi-time Markov renewal chains and stratified renewal theorems Cambridge Tracts in Mathematics83

Reference 31

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.073674Z

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Observation d0692056-fbf2-4ba1-9a3c-bd6b168f0762 · outbound

This paper cites Lamperti.

Multi-time Markov renewal chains and stratified renewal theorems Lamperti

Reference 32

Resolution: metadata mismatch; arxiv_id, observed 2026-07-09T16:16:20.049605Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7d0b15c3-ba9c-455f-ad0b-a0f9fac77397 · outbound

This paper cites Asymptotically optimal tests for mu ltinomial distributions.

Multi-time Markov renewal chains and stratified renewal theorems Asymptotically optimal tests for mu ltinomial distributions

Reference 33

Resolution: metadata mismatch; arxiv_id, observed 2026-07-09T16:16:20.071574Z

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Observation e365892c-6249-46d8-95a4-a4a938555313 · outbound

This paper cites On Bivariate Lack of Memory Property and a New Definition.Annals of the Institute of Statistical Mathematics54(2)404–410.

Multi-time Markov renewal chains and stratified renewal theorems On Bivariate Lack of Memory Property and a New Definition.Annals of the Institute of Statistical Mathematics54(2)404–410

Reference 34

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.035999Z

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Observation d4c1c6ba-fbeb-4d59-847c-70e26a41a88e · outbound

This paper cites an unresolved cited work.

Multi-time Markov renewal chains and stratified renewal theorems Unresolved cited work

Reference 35

Resolution: verified exact; doi, observed 2026-07-09T16:16:20.071488Z

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Observation ce0983be-c437-42bf-9edb-9848f274225f · outbound

This paper cites T1−1X n=T0 g(Jn, Jn+1, Xn+1)1{Sn−ST0=u} # , u∈N d, L. Kordalis and S. Trevezas/Multi-time Markov renewal chains56 we have, for 0< θ 2 < θ3 < θ1, X u∈Nd eθ2|u|1 |rg|(u)≤E a.

Multi-time Markov renewal chains and stratified renewal theorems T1−1X n=T0 g(Jn, Jn+1, Xn+1)1{Sn−ST0=u} # , u∈N d, L. Kordalis and S. Trevezas/Multi-time Markov renewal chains56 we have, for 0< θ 2 < θ3 < θ1, X u∈Nd eθ2|u|1 |rg|(u)≤E a

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-07-09T16:16:20.080152Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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