Erhard, Dirk; Reis, Guilherme Stochastic processes with competing reinforcements. (English) Zbl 07927495 Ann. Appl. Probab. 34, No. 5, 4513-4553 (2024). MSC: 60K35 60G50 60K37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Poudevigne-Auboiron, Rémy Monotonicity and phase transition for the VRJP and the ERRW. (English) Zbl 1545.60119 J. Eur. Math. Soc. (JEMS) 26, No. 3, 789-816 (2024). Reviewer: Janosch Ortmann (Montréal) MSC: 60K35 60K37 82B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Poudevigne-Auboiron, Rémy Limit theorem for sub-ballistic random walks in Dirichlet environment in dimension \(d \geq 3\). (English) Zbl 1534.60152 Electron. J. Probab. 29, Paper No. 51, 66 p. (2024). MSC: 60K35 60K37 60F17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rosales-Ortiz, Alejandro Noise reinforced Lévy processes: Lévy-Itô decomposition and applications. (English) Zbl 1528.60040 Electron. J. Probab. 28, Paper No. 161, 58 p. (2023). MSC: 60G50 60G51 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Jiaming; Laulin, Lucile Analysis of the smoothly amnesia-reinforced multidimensional elephant random walk. (English) Zbl 1523.60080 J. Stat. Phys. 190, No. 10, Paper No. 158, 42 p. (2023). MSC: 60G50 60F05 60G42 60F15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Prado, Fernando P. A.; Coletti, Cristian F.; Rosales, Rafael A. Two repelling random walks on \(\mathbb{Z}\). (English) Zbl 1511.60150 Stochastic Processes Appl. 160, 72-88 (2023). MSC: 60K35 37C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Andriopoulos, George; Archer, Eleanor Scaling limit of linearly edge-reinforced random walks on critical Galton-Watson trees. (English) Zbl 1514.60054 Electron. J. Probab. 28, Paper No. 9, 64 p. (2023). Reviewer: Pavel Stoynov (Sofia) MSC: 60G50 60F17 60K37 60K50 60J60 60J80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Xue, Ling; Zhang, Min; Zhao, Kun; Zheng, Xiaoming Global stability under dynamic boundary conditions of a nonlinear PDE model arising from reinforced random walks. (English) Zbl 1502.35183 Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106913, 14 p. (2023). MSC: 35Q92 35B35 × Cite Format Result Cite Review PDF Full Text: DOI
Erhard, Dirk; Franco, Tertuliano; Reis, Guilherme The directed edge reinforced random walk: the Ant Mill phenomenon. (English) Zbl 1508.60097 J. Stat. Phys. 190, No. 1, Paper No. 18, 18 p. (2023). MSC: 60K35 60K37 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bertenghi, Marco; Rosales-Ortiz, Alejandro Joint invariance principles for random walks with positively and negatively reinforced steps. (English) Zbl 1504.60072 J. Stat. Phys. 189, No. 3, Paper No. 35, 31 p. (2022). MSC: 60G50 60G51 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rosales, Rafael A.; Prado, Fernando P. A.; Pires, Benito Vertex reinforced random walks with exponential interaction on complete graphs. (English) Zbl 1492.60289 Stochastic Processes Appl. 148, 353-379 (2022). MSC: 60K35 37C10 60J10 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Laulin, Lucile New insights on the reinforced elephant random walk using a martingale approach. (English) Zbl 1490.60108 J. Stat. Phys. 186, No. 1, Paper No. 9, 23 p. (2022). MSC: 60G50 60G42 60F17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Pfaffelhuber, Peter; Stiefel, Jakob The range of once-reinforced random walk in one dimension. (English) Zbl 1523.60083 Random Struct. Algorithms 58, No. 1, 164-175 (2021). MSC: 60G50 05C81 60F05 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kious, Daniel; Schapira, Bruno; Singh, Arvind Once reinforced random walk on \(\mathbb{Z}\times\gamma\). (English. French summary) Zbl 1487.60188 Ann. Inst. Henri Poincaré, Probab. Stat. 57, No. 4, 2219-2242 (2021). MSC: 60K35 60G50 60K37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Huang, Xiangyu; Liu, Yong; Sidoravicius, Vladas; Xiang, Kainan A note on once reinforced random walk on ladder \(\mathbb{Z} \times \{0, 1 \} \). (English) Zbl 1483.60147 Electron. Commun. Probab. 26, Paper No. 38, 12 p. (2021). MSC: 60K35 × Cite Format Result Cite Review PDF Full Text: DOI
Schapira, Bruno Localization on 5 sites for vertex reinforced random walks: towards a characterization. (English) Zbl 1479.60202 Ann. Appl. Probab. 31, No. 4, 1774-1786 (2021). MSC: 60K35 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link HAL
Fribergh, Alexander; Kious, Daniel; Sidoravicius, Vladas; Stauffer, Alexandre Random memory walk. (English) Zbl 1469.60327 Vares, Maria Eulália (ed.) et al., In and out of equilibrium 3: celebrating Vladas Sidoravicius. Cham: Birkhäuser. Prog. Probab. 77, 439-453 (2021). MSC: 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kozma, Gady; Peled, Ron Power-law decay of weights and recurrence of the two-dimensional VRJP. (English) Zbl 1478.60265 Electron. J. Probab. 26, Paper No. 82, 19 p. (2021). MSC: 60K35 60K37 81T25 81T60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dinh, Thu; Xin, Jack Enhanced diffusivity in perturbed senile reinforced random walk models. (English) Zbl 1472.35291 Asymptotic Anal. 122, No. 1-2, 87-104 (2021). MSC: 35Q35 76F99 82C41 82C31 60G50 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fasino, Dario; Tudisco, Francesco Ergodicity coefficients for higher-order stochastic processes. (English) Zbl 1483.60105 SIAM J. Math. Data Sci. 2, No. 3, 740-769 (2020). MSC: 60J10 60G50 65C30 65F35 65C40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bonilla, Luis L.; Carretero, Manuel; Terragni, Filippo Integrodifference master equation describing actively growing blood vessels in angiogenesis. (English) Zbl 07446864 Int. J. Nonlinear Sci. Numer. Simul. 21, No. 7-8, 705-713 (2020). MSC: 92C15 92C30 39A99 60J85 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Holmes, Mark; Kious, Daniel A monotonicity property for once reinforced biased random walk on \(\mathbb{Z}^d\). (English) Zbl 1446.82030 Sidoravicius, Vladas (ed.), Sojourns in probability theory and statistical physics. III. Interacting particle systems and random walks, a festschrift for Charles M. Newman. Singapore: Springer; Shanghai: NYU Shanghai. Springer Proc. Math. Stat. 300, 255-273 (2019). MSC: 82B41 60J80 60J50 60K37 × Cite Format Result Cite Review PDF Full Text: DOI
Bonilla, Luis L.; Carretero, Manuel; Terragni, Filippo Stochastic models of blood vessel growth. (English) Zbl 1442.82009 Giacomin, Giambattista (ed.) et al., Stochastic dynamics out of equilibrium. Lecture notes from the IHP trimester, Institut Henri Poincaré (IHP), Paris, France, April – July, 2017. Cham: Springer. Springer Proc. Math. Stat. 282, 413-436 (2019). MSC: 82C20 82C41 82C31 60H10 60H15 34F05 92C15 92C17 35R09 × Cite Format Result Cite Review PDF Full Text: DOI
Serlet, Laurent Explicit laws for the records of the perturbed random walk on \(\mathbb{Z} \). (English) Zbl 1452.60029 Donati-Martin, Catherine (ed.) et al., Séminaire de probabilités XLIX. Cham: Springer. Lect. Notes Math. 2215, 495-519 (2018). MSC: 60G50 60F17 60J10 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Collevecchio, Andrea; Holmes, Mark; Kious, Daniel On the speed of once-reinforced biased random walk on trees. (English) Zbl 1417.60085 Electron. J. Probab. 23, Paper No. 86, 32 p. (2018). MSC: 60K37 60G50 60J80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Chen, Xinxin; Zeng, Xiaolin Speed of vertex-reinforced jump process on Galton-Watson trees. (English) Zbl 1429.60067 J. Theor. Probab. 31, No. 2, 1166-1211 (2018). MSC: 60J80 60K37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Kious, Daniel; Sidoravicius, Vladas Phase transition for the once-reinforced random walk on \(\mathbb{Z}^{d}\)-like trees. (English) Zbl 1429.60074 Ann. Probab. 46, No. 4, 2121-2133 (2018). MSC: 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Le Goff, Line C.; Raimond, Olivier Vertex reinforced non-backtracking random walks: an example of path formation. (English) Zbl 1430.60086 Electron. J. Probab. 23, Paper No. 39, 38 p. (2018). MSC: 60K35 60G99 91C99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Cénac, Peggy; Le Ny, Arnaud; de Loynes, Basile; Offret, Yoann Persistent random walks. I. Recurrence versus transience. (English) Zbl 1390.60165 J. Theor. Probab. 31, No. 1, 232-243 (2018). MSC: 60G50 60G17 60J05 37B20 60K35 × Cite Format Result Cite Review PDF Full Text: DOI Link
Chloé Le Goff, Line; Soulier, Philippe Parameter estimation of a two-colored urn model class. (English) Zbl 07941807 Int. J. Biostat. 13, No. 1, Article ID 20160029, 24 p. (2017). MSC: 62P10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sabot, Christophe; Tarrès, Pierre; Zeng, Xiaolin The vertex reinforced jump process and a random Schrödinger operator on finite graphs. (English) Zbl 06838112 Ann. Probab. 45, No. 6A, 3967-3986 (2017). MSC: 60K37 60K35 82B44 81T25 81T60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Cotar, Codina; Thacker, Debleena Edge- and vertex-reinforced random walks with super-linear reinforcement on infinite graphs. (English) Zbl 1418.60036 Ann. Probab. 45, No. 4, 2655-2706 (2017). MSC: 60G50 60J10 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Benson, Austin R.; Gleich, David F.; Lim, Lek-Heng The spacey random walk: a stochastic process for higher-order data. (English) Zbl 1365.15033 SIAM Rev. 59, No. 2, 321-345 (2017). MSC: 15A69 65C50 60G50 60J10 15B51 15A18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bacallado, Sergio; Pande, Vijay; Favaro, Stefano; Trippa, Lorenzo Bayesian regularization of the length of memory in reversible sequences. (English) Zbl 1414.62084 J. R. Stat. Soc., Ser. B, Stat. Methodol. 78, No. 4, 933-946 (2016). MSC: 62F15 60J10 62M05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Sabot, Christophe; Tarrès, Pierre Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model. (English) Zbl 1331.60185 J. Eur. Math. Soc. (JEMS) 17, No. 9, 2353-2378 (2015). Reviewer: Marius Iosifescu (Bucureşti) MSC: 60K37 60G50 60K35 60J75 81T25 81T60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Disertori, Margherita; Sabot, Christophe; Tarrès, Pierre Transience of edge-reinforced random walk. (English) Zbl 1329.60116 Commun. Math. Phys. 339, No. 1, 121-148 (2015). Reviewer: Martynas Manstavičius (Vilnius) MSC: 60G50 60J75 60K37 60K35 05C81 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas Monotone interaction of walk and graph: recurrence versus transience. (English) Zbl 1307.60140 Electron. Commun. Probab. 19, Paper No. 76, 12 p. (2014). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Jun Two particles’ repelling random walks on the complete graph. (English) Zbl 1307.60048 Electron. J. Probab. 19, Paper No. 113, 17 p. (2014). MSC: 60G50 60K35 05C81 37C10 × Cite Format Result Cite Review PDF Full Text: DOI
Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas Walking within growing domains: recurrence versus transience. (English) Zbl 1307.60149 Electron. J. Probab. 19, Paper No. 106, 20 p. (2014). MSC: 60K37 60K35 82C24 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Jun; Kozma, Gady Vertex-reinforced random walk on \(\mathbb Z\) with sub-square-root weights is recurrent. (Récurrence d’une marche aléatoire renforcée par sommets sur \(\mathbb Z\) avec poids inférieur à racine carrée.) (English. French summary) Zbl 1307.60049 C. R., Math., Acad. Sci. Paris 352, No. 6, 521-524 (2014). Reviewer: Boris Granovsky (Haifa) MSC: 60G50 60J27 60J28 60F20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Percus, Jerome K.; Percus, Ora E. Reinforced Brownian motion: a prototype. (English) Zbl 1302.82054 J. Stat. Phys. 156, No. 5, 917-931 (2014). MSC: 82B41 60J65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Basdevant, Anne-Laure; Schapira, Bruno; Singh, Arvind Localization on 4 sites for vertex-reinforced random walks on \(\mathbb{Z}\). (English) Zbl 1297.60062 Ann. Probab. 42, No. 2, 527-558 (2014). Reviewer: Chen Mu-Fa (Beijing) MSC: 60K35 60G50 60J20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Kozma, Gady Reinforced random walk. (English) Zbl 1364.60135 Latała, Rafał (ed.) et al., European Congress of Mathematics. Proceedings of the 6th ECM congress, Kraków, Poland, July 2–7 July, 2012. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-120-0/hbk). 429-443 (2013). MSC: 60K35 60K37 60G50 60G09 60J10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Horger, Thomas; Oelker, Aenne; Kuttler, Christina; Pérez-Velázquez, Judith Mathematical modeling of tumor-induced angiogenesis using porous medium diffusion. (English) Zbl 1331.92023 Int. J. Biomath. Biostat. 2, No. 2, 145-165 (2013). MSC: 92C15 92C50 35Q92 × Cite Format Result Cite Review PDF
Rao, K. Balaji; Anoop, M. B. Why do we need probability distributions with fat tails to describe the surface strain evolution in reinforced concrete flexural members? (English) Zbl 1293.74434 Meccanica 48, No. 6, 1517-1542 (2013). MSC: 74S60 74E30 × Cite Format Result Cite Review PDF Full Text: DOI
Budhiraja, Amarjit; Del Moral, Pierre; Rubenthaler, Sylvain Discrete time Markovian agents interacting through a potential. (English) Zbl 1374.60126 ESAIM, Probab. Stat. 17, 614-634 (2013). MSC: 60J05 60K35 92C45 70K20 60K40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bouchet, Élodie Sub-ballistic random walk in Dirichlet environment. (English) Zbl 1296.60267 Electron. J. Probab. 18, Paper No. 58, 25 p. (2013). MSC: 60K37 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Benaim, Michel; Raimond, Olivier; Schapira, Bruno Strongly vertex-reinforced-random-walk on a complete graph. (English) Zbl 1277.60169 ALEA, Lat. Am. J. Probab. Math. Stat. 10, No. 2, 767-782 (2013). MSC: 60K35 × Cite Format Result Cite Review PDF Full Text: arXiv
Sabot, Christophe Random Dirichlet environment viewed from the particle in dimension \(d\geq 3\). (English) Zbl 1269.60077 Ann. Probab. 41, No. 2, 722-743 (2013). MSC: 60K37 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Serlet, Laurent Hitting times for the perturbed reflecting random walk. (English) Zbl 1259.82045 Stochastic Processes Appl. 123, No. 1, 110-130 (2013). Reviewer: Utkir Rozikov (Tashkent) MSC: 82B41 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Schapira, Bruno A 0-1 law for vertex-reinforced random walks on \(\mathbb{Z}\) with weight of order \(k^\alpha,\;\alpha\in[0,1/2)\). (English) Zbl 1244.60033 Electron. Commun. Probab. 17, Paper No. 22, 8 p. (2012). MSC: 60F20 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
van der Hofstad, Remco; Holmes, Mark An expansion for self-interacting random walks. (English) Zbl 1238.60116 Braz. J. Probab. Stat. 26, No. 1, 1-55 (2012). Reviewer: Stella Kapodistria (Eindhoven) MSC: 60K37 82B41 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merkl, Franz; Rolles, Silke W. W. Correlation inequalities for edge-reinforced random walk. (English) Zbl 1243.60018 Electron. Commun. Probab. 16, 753-763 (2011). MSC: 60E15 82B41 60K35 × Cite Format Result Cite Review PDF Full Text: DOI
Collevecchio, Andrea; Schmitz, Tom Bounds on the speed and on regeneration times for certain processes on regular trees. (English) Zbl 1225.60156 Ann. Appl. Probab. 21, No. 3, 1073-1101 (2011). Reviewer: Dominique Lepingle (Orléans) MSC: 60K37 60K99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cohen, Netta; Jordan, Jonathan; Voliotis, Margaritis Preferential duplication graphs. (English) Zbl 1216.05142 J. Appl. Probab. 47, No. 2, 572-585 (2010). Reviewer: David B. Penman (Colchester) MSC: 05C80 60G99 60K35 × Cite Format Result Cite Review PDF Full Text: DOI
Cotar, Codina; Limic, Vlada Attraction time for strongly reinforced walks. (English) Zbl 1213.60087 Ann. Appl. Probab. 19, No. 5, 1972-2007 (2009). Reviewer: Alexander V. Bulinski (Moskva) MSC: 60G50 60J10 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merkl, Franz; Rolles, Silke W. W. Recurrence of edge-reinforced random walk on a two-dimensional graph. (English) Zbl 1180.82085 Ann. Probab. 37, No. 5, 1679-1714 (2009). Reviewer: Guy Jumarie (Montréal) MSC: 82B41 60K35 60K37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merkl, Franz; Rolles, Silke W. W. Edge-reinforced random walk on one-dimensional periodic graphs. (English) Zbl 1186.82039 Probab. Theory Relat. Fields 145, No. 3-4, 323-349 (2009). Reviewer: Achim Klenke (Mainz) MSC: 82B41 60K35 60K37 × Cite Format Result Cite Review PDF Full Text: DOI
Merkl, Franz; Rolles, Silke W. W. Bounding a random environment bounding a random environment for two-dimensional edge-reinforced random walk. (English) Zbl 1187.82051 Electron. J. Probab. 13, 530-565 (2008). MSC: 82B41 60K35 60K37 × Cite Format Result Cite Review PDF Full Text: DOI EuDML EMIS
Takei, Masato; Takeshima, Masaki Phase diagram for once-reinforced random walks on trees with exponential weighting scheme. (English) Zbl 1202.60068 Stat. Probab. Lett. 78, No. 17, 3000-3007 (2008). Reviewer: Wolfgang König (Leipzig) MSC: 60G50 60K35 × Cite Format Result Cite Review PDF Full Text: DOI
Myjak, Józef; Rudnicki, Ryszard Reinforced walk on graphs and neural networks. (English) Zbl 1154.60360 Stud. Math. 189, No. 3, 255-268 (2008). MSC: 60K37 60J10 60J20 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI
Sellke, T. Reinforced random walk on the \(d\)-dimensional integer lattice. (English) Zbl 1154.82011 Markov Process. Relat. Fields 14, No. 2, 291-308 (2008). Reviewer: Achim Klenke (Mainz) MSC: 82B41 60K35 × Cite Format Result Cite Review PDF
Aidékon, Elie Transient random walks in random environment on a Galton-Watson tree. (English) Zbl 1146.60078 Probab. Theory Relat. Fields 142, No. 3-4, 525-559 (2008). MSC: 60K37 60J80 60F15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kovchegov, Yevgeniy Multi-particle processes with reinforcements. (English) Zbl 1141.60071 J. Theor. Probab. 21, No. 2, 437-448 (2008). MSC: 60K37 60C05 60G07 60G09 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pemantle, Robin A survey of random processes with reinforcement. (English) Zbl 1189.60138 Probab. Surv. 4, 1-79 (2007). MSC: 60J20 60G50 37A50 60K40 60-02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML
Limic, Vlada; Tarrès, Pierre Attracting edge and strongly edge reinforced walks. (English) Zbl 1131.60036 Ann. Probab. 35, No. 5, 1783-1806 (2007). Reviewer: Alexander V. Bulinskij (Moskva) MSC: 60G50 60J10 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merkl, Franz; Rolles, Silke W. W. A random environment for linearly edge-reinforced random walks on infinite graphs. (English) Zbl 1116.60060 Probab. Theory Relat. Fields 138, No. 1-2, 157-176 (2007). MSC: 60K37 60K35 × Cite Format Result Cite Review PDF Full Text: DOI Link
Merkl, Franz; Rolles, Silke W. W. Linearly edge-reinforced random walks. (English) Zbl 1125.82014 Denteneer, Dee (ed.) et al., Dynamics and stochastics. Festschrift in honor of M. S. Keane. Selected papers based on the presentations at the conference ‘Dynamical systems, probability theory, and statistical mechanics’, Eindhoven, The Netherlands, January 3–7, 2005, on the occasion of the 65th birthday of Mike S. Keane. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-64-1/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 48, 66-77 (2006). MSC: 82B41 60K35 60K37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Collevecchio, Andrea On the transience of processes defined on Galton-Watson trees. (English) Zbl 1104.60048 Ann. Probab. 34, No. 3, 870-878 (2006). MSC: 60J80 60G50 60J75 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merkl, Franz; Rolles, Silke W. W. Edge-reinforced random walk on a ladder. (English) Zbl 1102.82010 Ann. Probab. 33, No. 6, 2051-2093 (2005). Reviewer: Utkir Rozikov (Tashkent) MSC: 82B41 60K35 60K37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sabot, Christophe Markov chains in a Dirichlet environment and hypergeometric integrals. (English) Zbl 1087.60078 C. R., Math., Acad. Sci. Paris 342, No. 1, 57-62 (2005). Reviewer: Yuri Kozitsky (Lublin) MSC: 60K37 82D30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dai, Jack Jie Some results regarding vertex-reinforced random walks. (English) Zbl 1102.60040 Stat. Probab. Lett. 66, No. 3, 259-266 (2004). MSC: 60G50 × Cite Format Result Cite Review PDF Full Text: DOI
Volkov, Stanislav Excited random walk on trees. (English) Zbl 1065.60097 Electron. J. Probab. 8, Paper No. 23, 15 p. (2003). MSC: 60J10 60G50 × Cite Format Result Cite Review PDF Full Text: DOI EuDML EMIS
Limic, Vlada Attracting edge property for a class of reinforced random walks. (English) Zbl 1057.60048 Ann. Probab. 31, No. 3, 1615-1654 (2003). Reviewer: Wolfgang König (Leipzig) MSC: 60G50 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Plank, M. J.; Sleeman, B. D. A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. (English) Zbl 1044.92036 Math. Med. Biol. 20, No. 2, 135-181 (2003). MSC: 92C50 60G50 35Q92 × Cite Format Result Cite Review PDF Full Text: DOI
Dai, Jack Jie A note on vertex-reinforced random walks. (English) Zbl 1116.60331 Stat. Probab. Lett. 62, No. 3, 275-280 (2003). MSC: 60G50 60G42 × Cite Format Result Cite Review PDF Full Text: DOI
Rolles, Silke W. W. How edge-reinforced random walk arises naturally. (English) Zbl 1029.60089 Probab. Theory Relat. Fields 126, No. 2, 243-260 (2003). Reviewer: A.Pellegrinotti (Roma) MSC: 60K37 60G09 × Cite Format Result Cite Review PDF Full Text: DOI
Plank, M. J.; Sleeman, B. D.; Jones, P. F. A mathematical model of an In Vitro experiment to investigate endothelial cell migration. (English) Zbl 1052.92022 J. Theor. Med. 4, No. 4, 251-270 (2002). MSC: 92C37 92C50 60G50 92C17 60G35 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Keane, M. S.; Rolles, S. W. W. Tubular recurrence. (English) Zbl 1026.60089 Acta Math. Hung. 97, No. 3, 207-221 (2002). Reviewer: S.K.Srinivasan (Chennai) MSC: 60J10 05C99 60K37 × Cite Format Result Cite Review PDF Full Text: DOI
Durrett, Rick; Kesten, Harry; Limic, Vlada Once edge-reinforced random walk on a tree. (English) Zbl 0995.60042 Probab. Theory Relat. Fields 122, No. 4, 567-592 (2002). MSC: 60G50 60K99 × Cite Format Result Cite Review PDF Full Text: DOI
Volkov, Stanislav Vertex-reinforced random walk on arbitrary graphs. (English) Zbl 1031.60089 Ann. Probab. 29, No. 1, 66-91 (2001). Reviewer: Nina Gantert (Karlsruhe) MSC: 60K37 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Takeshima, Masaki Estimates of hitting probabilities for a 1-dimensional reinforced random walk. (English) Zbl 0992.60071 Osaka J. Math. 38, No. 4, 693-709 (2001). Reviewer: Thomas Simon (Évry) MSC: 60J10 × Cite Format Result Cite Review PDF
Takeshima, Masaki Behavior of 1-dimensional reinforced random walk. (English) Zbl 0962.60017 Osaka J. Math. 37, No. 2, 355-372 (2000). Reviewer: Gheorghe Oprişan (Bucureşti) MSC: 60G50 60J10 60F05 × Cite Format Result Cite Review PDF
Rudnicki, Ryszard; Wolf, Marek Random walk with memory. (English) Zbl 0953.60080 J. Math. Phys. 40, No. 6, 3072-3083 (1999). Reviewer: G.Oprişan (Bucureşti) MSC: 60J99 60J10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Davis, Burgess Brownian motion and random walk perturbed at extrema. (English) Zbl 0930.60041 Probab. Theory Relat. Fields 113, No. 4, 501-518 (1999). MSC: 60G50 60F05 60J65 82C41 × Cite Format Result Cite Review PDF Full Text: DOI
Horváth, Lajos; Shao, Qi-Man Limit distributions of directionally reinforced random walks. (English) Zbl 0911.60008 Adv. Math. 134, No. 2, 367-383 (1998). Reviewer: L.G.Gorostiza (Mexico City) MSC: 60F05 60G50 60K40 × Cite Format Result Cite Review PDF Full Text: DOI
Davis, Burgess Perturbed random walks and Brownian motions, and local times. (English) Zbl 0903.60054 New York J. Math. 3A, 81-87 (1998). Reviewer: A.Khorunzhy (Khar’kov) MSC: 60G50 60F05 60J65 82C41 × Cite Format Result Cite Review PDF Full Text: EuDML EMIS
Tóth, B. Limit theorems for weakly reinforced random walks on \(\mathbb{Z}\). (English) Zbl 0912.60043 Stud. Sci. Math. Hung. 33, No. 1-3, 321-337 (1997). Reviewer: Petr Lachout (Praha) MSC: 60F05 60J55 82C41 60G50 × Cite Format Result Cite Review PDF
Othmer, Hans G.; Stevens, Angela Aggregation, blowup, and collapse: the ABC’s of taxis in reinforced random walks. (English) Zbl 0990.35128 SIAM J. Appl. Math. 57, No. 4, 1044-1081 (1997). MSC: 35Q80 60J99 92B05 × Cite Format Result Cite Review PDF Full Text: DOI
Davis, B. Reinforced random walk. (English) Zbl 0665.60077 Probab. Theory Relat. Fields 84, No. 2, 203-229 (1990). Reviewer: B.Davis MSC: 60J65 60J45 30C85 × Cite Format Result Cite Review PDF Full Text: DOI