Ergodicity of p−majorizing nonlinear Markov operators on the finite dimensional space

Badocha, 2018, Quadratic stochastic operators on Banach lattices, Positivity, 22, 477, 10.1007/s11117-017-0522-9 Bartoszek, 2017, Weak stability of centred quadratic stochastic operators, Bull. Malays. Math. Sci. Soc. Bartoszek, 2013, Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait, 19 Bartoszeka, 2015, Asymptotic properties of quadratic stochastic operators acting on the L1 space, Nonlinear Anal., 114, 26, 10.1016/j.na.2014.10.032 Bartoszek, 2018, Prevalence problem in the set of quadratic stochastic operators acting on L1, Bull. Malays. Math. Sci. Soc., 41, 159, 10.1007/s40840-015-0245-7 Bartoszek, 2013, On mixing in the class of quadratic stochastic operators, Nonlinear Anal., 86, 95, 10.1016/j.na.2013.03.011 Bernstein, 1942, Solution of a mathematical problem connected with the theory of heredity, Ann. Math. Stat., 13, 53, 10.1214/aoms/1177731642 Chang, 2016, Polytopes of stochastic tensors, Ann. Funct. Anal., 7, 386, 10.1215/20088752-3605195 Cui, 2014, Birkhoff–von Neumann theorem for multistochastic tensors, SIAM J. Matrix Anal. Appl., 35, 956, 10.1137/120896499 Frank, 2005 Ganihodzhaev, 1991, On stochastic processes generated by quadratic operators, J. Theoret. Probab., 4, 639, 10.1007/BF01259547 Ganikhodjaev, 2015, Quadratic stochastic operators and zero-sum game dynamics, Ergodic Theory Dynam. Systems, 35, 1443, 10.1017/etds.2013.109 Ganikhodjaev, 2006, On the ergodic principle for Markov and quadratic stochastic processes and its relations, Linear Algebra Appl., 416, 730, 10.1016/j.laa.2005.12.032 Ganikhodjaev, 2004, On a necessary condition for the ergodicity of quadratic operators defined on the two-dimensional simplex, Russian Math. Surveys, 59, 571, 10.1070/RM2004v059n03ABEH000744 Ganikhodzhaev, 1992, On the definition of quadratic doubly stochastic operators, Russian Math. Surveys, 48, 244, 10.1070/RM1993v048n04ABEH001058 Ganikhodzhaev, 2011, Quadratic stochastic operators and processes: results and open problems, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 14, 279, 10.1142/S0219025711004365 Gleich, 2015, Multilinear pagerank, SIAM J. Matrix Anal. Appl., 36, 1507, 10.1137/140985160 Hartfiel, 1974, A study of convex sets of stochastic matrices induced by probability vectors, Pacific J. Math., 52, 405, 10.2140/pjm.1974.52.405 Hu, 2014, Convergence of a second order Markov chain, Appl. Math. Comput., 241, 183 Joe, 1990, Majorization and divergence, J. Math. Anal. Appl., 148, 287, 10.1016/0022-247X(90)90002-W Ke, 2016, Characterization of extreme points of multistochastic tensors, Comput. Methods Appl. Math., 16, 459, 10.1515/cmam-2016-0005 Kesten, 1970, Quadratic transformations: a model for population growth I, Adv. in Appl. Probab., 2, 1, 10.2307/3518344 Kolokoltsov, 2010 Leizarowitz, 1992, On infinite products of stochastic matrices, Linear Algebra Appl., 168, 189, 10.1016/0024-3795(92)90294-K Li, 2017, The uniqueness of multilinear PageRank vectors, Numer. Linear Algebra Appl., 24, 10.1002/nla.2107 Li, 2014, On the limiting probability distribution of a transition probability tensor, Linear Multilinear Algebra, 62, 362, 10.1080/03081087.2013.777436 Li, 2015, Stationary probability vectors of higher-order Markov chains, Linear Algebra Appl., 473, 114, 10.1016/j.laa.2014.03.043 Li, 2017, On the number of vertices of the stochastic tensor polytope, Linear Multilinear Algebra, 65, 2064, 10.1080/03081087.2017.1310178 Lyubich, 1992 Marshall, 2011 McKean, 1966, A class of Markov processes associated with nonlinear parabolic equations, Proc. Natl. Acad. Sci. USA, 56, 1907, 10.1073/pnas.56.6.1907 Mukhamedov, 2015 Paz, 1971 Pulka, 2011, On the mixing property and the ergodic principle for non-homogeneous Markov chains, Linear Algebra Appl., 434, 1475, 10.1016/j.laa.2010.11.021 Qi, 2017 Saburov, 2015, A class of nonergodic Lotka–Volterra operators, Math. Notes, 97, 759, 10.1134/S0001434615050107 Saburov, 2015, On divergence of any order Cesaro mean of Lotka–Volterra operators, Ann. Funct. Anal., 6, 247, 10.15352/afa/06-4-247 Saburov, 2016, Ergodicity of nonlinear Markov operators on the finite dimensional space, Nonlinear Anal., 143, 105, 10.1016/j.na.2016.05.006 Saburov, 2016, Quadratic stochastic Sarymsakov operators, J. Phys., Conf. Ser., 697 Saburov, 2017, On regularity of diagonally positive quadratic doubly stochastic operators, Results Math., 72, 1907, 10.1007/s00025-017-0723-3 Saburov, 2018, On regularity of positive quadratic doubly stochastic operators, Math. Notes, 103, 328, 10.1134/S0001434618010376 Saburov, 2018, Ergodicity of p−majorizing quadratic stochastic operators, Markov Process. Related Fields, 24, 131 Saburov, 2018, Dichotomy of iterated means for nonlinear operators, Funct. Anal. Appl., 52, 74, 10.1007/s10688-018-0212-9 Saburov, 2014, Mathematical models of nonlinear uniform consensus, Science Asia, 40, 306, 10.2306/scienceasia1513-1874.2014.40.306 Saburov, 2014, Reaching a nonlinear consensus: polynomial stochastic operators, Int. J. Control Autom. Syst., 12, 1276, 10.1007/s12555-014-0061-0 Saburov, 2016, Reaching a consensus: a discrete nonlinear time-varying case, Internat. J. Systems Sci., 47, 2449, 10.1080/00207721.2014.998743 Saburov, 2017, Reaching nonlinear consensus via non-autonomous polynomial stochastic operators, J. Phys., Conf. Ser., 819, 10.1088/1742-6596/819/1/012009 Saburov, 2017, Reaching consensus via polynomial stochastic operators: a general study, Springer Proc. Math. Stat., 212, 219 Saburov, 2016, On quadratic stochastic operators having three fixed points, J. Phys., Conf. Ser., 697 Saburov, 2016, Counterexamples to the conjecture on stationary probability vectors of the second-order Markov chains, Linear Algebra Appl., 507, 153, 10.1016/j.laa.2016.06.012 Saburov, 2018, The structure of the fixed point set of quadratic operators on the simplex, Fixed Point Theory, 19, 383, 10.24193/fpt-ro.2018.1.30 Sarymsakov, 1961, Inhomogeneous Markov chains, Theory Probab. Appl., 6, 178, 10.1137/1106022 Sarymsakov, 1990, Analytic methods in the theory of quadratic stochastic processes, J. Theoret. Probab., 3, 51, 10.1007/BF01063328 Seneta, 1973, On strong ergodicity of inhomogeneous products of finite stochastic matrices, Studia Math., 46, 241, 10.4064/sm-46-3-241-247 Seneta, 1979, Coefficients of ergodicity: structure and applications, Adv. Probab., 11, 576, 10.2307/1426955 Seneta, 1981 Ulam, 1960 Wolfowitz, 1963, Products of indecomposable, aperiodic, stochastic matrices, Proc. Amer. Math. Soc., 14, 733, 10.1090/S0002-9939-1963-0154756-3