Markov processes, non-Archimedean analysis, nonlocal operators, p-adic numbers

[1] Avetisov VA, Bikulov A Kh. Ultrametricity of fluctuation dynamic mobility of protein molecules, Proceedings of the Steklov Institute of Mathematics, 265: 75-81, 2009. (Russian), Trudy Matematicheskogo Instituta imeni V.A. Steklova, 265: 82-89, 2009.
doi: 10.1134/S0081543809020060

[2] Avetisov VA, Bikulov AKh, Zubarev AP. First passage time distribution and the number of returns for ultrametric random walks, Journal of Physics A: Mathematical and Theoretical, 42(8): 085003, 2009.
doi: 10.1088/1751-8113/42/8/085003

[3] Avetisov VA, Bikulov AKh, Osipov VA. p-adic models of ultrametric diffusion in conformational dynamics of macromolecules. (Russian), Trudy Matematicheskogo Instituta imeni V.A. Steklova, 245(2): 55-64, 2004

[4] Avetisov VA, Bikulov AKh, Osipov VA. p-adic description of characteristic relaxation in complex systems, Journal of Physics A: Mathematical and General, 36 (15): 4239-4246, 2003.
doi: 10.1088/0305-4470/36/15/301

[5] Avetisov VA, Bikulov AH, Kozyrev SV, Osipov VA. p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes, Journal of Physics A: Mathematical and General, 35(2): 177-189, 2002.
doi: 10.1088/0305-4470/35/2/301

[6] Avetisov VA, Bikulov AKh, Kozyrev SV. Description of logarithmic relaxation by a model of a hierarchical random walk. (Russian), Doklady Akademii Nauk, 368(2): 164-167, 1999.

[7] Dragovich B, Khrennikov AYu, Kozyrev SV, Volovich IV. On p-adic mathematical physics, p-Adic Numbers Ultrametric Analysis and Applications, 1(1): 1-17, 2009.
doi: 10.1134/S2070046609010014

[8] Khrennikov AYu, Kozyrev SV. p-adic pseudodifferential operators and analytic continuation of replica matrices, Theoretical and Mathematical Physics, 144(2): 1166-1170, 2005.
doi: 10.4213/tmf1858

[9] Mezard M, Parisi G, Virasoro MA. Spin glass theory and beyond, In World Scientific Lecture Notes in Physics, 1987.
doi: 10.1142/0271

[10] Varadarajan VS. Path integrals for a class of p-adic Schrodinger equations, Letters in Mathematical Physics, 39 (2): 97-106, 1997.
doi: 10.1023/A:1007364631796

[11] Vladimirov VS, Volovich IV, Zelenov EI. p-analysis and mathematical physics, World Scientific, 1994.

[12] Zúñiga-Galindo WA. Parabolic equations and Markov processes over p-adic fields, Potential Analysis, 28 (2): 185-200, 2008.
doi: 10.1007/s11118-007-9072-2

[13] Galeano-Peñaloza J, Zúñiga-GalindoWA. Pseudo-differential operators with semi-quasielliptic symbols over p-adic fields, Journal of Mathematical Analysis and Applications, 386 (1): 32-49, 2012.
doi: 10.1016/j.jmaa.2011.07.040

[14] KarwowskiW. Diffusion processes with ultrametric jumps, Reports on Mathematical Physics, 60 (2): 221-235, 2007.
doi: 10.1016/S0034-4877(07)00025-0

[15] Rammal R, Toulouse G, Virasoro MA. Ultrametricity for physicists, Reviews of Modern Physics, 58 (3): 765-788, 1986.
doi: 10.1103/RevModPhys.58.765

[16] Kochubei AN. Pseudo-differential equations and stochastics over non-Archimedean fields, Monographs and Textbooks in Pure and Applied Mathematics, 244, Marcel Dekker, Inc., New York, 2001.

[17] Chacón-Cortés LF, Zúñiga-Galindo WA. Non-local operators, non-Archimedean parabolic-type equations with variable coefficients and Markov processes, Publications of the Research Institute for Mathematical Sciences PRIMS, 51 (2): 289-317, 2015.
doi: 10.4171/PRIMS/156

[18] Chacón-Cortés LF, Zúñiga-GalindoWA. Nonlocal operators, parabolictype equations, and ultrametric random walks, Journal of Mathematical Physics, 54 (11): 113503, 2013.
doi: 10.1063/1.4828857

[19] Casas-Sánchez OF, Galeano-Peñaloza J, Rodríguez-Vega JJ. Parabolictype pseudodifferential equations with elliptic symbols in dimension 3 over p-adics, p-Adic Numbers Ultrametric Analysis and Applications, 7(1): 1-16, 2015.
doi: 10.1134/S207004661501001X

[20] Chacón-Cortés LF. The problem of the first passage time for some elliptic pseudodiffe-rential operators over the p-adics, Revista Colombiana de Matemáticas, 48 (2): 191-209, 2014.
doi: 10.15446/recolma.v48n2.54124

[21] Casas-Sánchez OF, Galeano-Peñaloza J, Rodríguez-Vega JJ. The problem of the first return attached to a pseudodifferential operator in dimension 3, Revista Integración. Temas Matemáticos, 33(2): 107-119, 2015.
doi: 10.18273/revint.v33n2-2015002

[22] Casas-Sánchez OF, Zúñiga-Galindo WA. p-adic elliptic quadratic forms, parabolic-type pseudodifferential equations with variable coefficients and Markov processes, p-Adic Numbers Ultrametric Analysis and Applications, 6 (1): 1-20, 2014.
doi: 10.1134/S2070046614010014

[23] Albeverio S, Khrennikov AYu, Shelkovich VM. Theory of p-adic distributions: linear and nonlinear models. Cambridge University Press, 2010.

[24] Taibleson MH. Fourier analysis on local fields, Princeton University Press, 1975.

[25] Zúñiga-Galindo WA. Pseudodifferential Equations Over Non-Archimedean Spaces, Lectures Notes in Mathematics vol. 2174, Springer, 2016.

[26] Berg C and Forst G. Potential theory on locally compact abelian groups, Springer-Verlag, New York, 1975.

[27] Engel K-J, Nagel R. One-Parameter Semigroups for Linear Evolution Equations. Springer-Verlag, 2000.

[28] Cazenave Thierry, Haraux Alain: An introduction to semilinear evolution equations. Oxford University Press, 1998.

[29] Torresblanca-Badillo A, Zúñiga-Galindo WA. Ultrametric Diffusion, Exponential Landscapes, and the First Passage Time Problem, Acta Applicandae Mathematicae, 157(1): 93-116, 2018.
doi: 10.1007/s10440-018-0165-2

[30] Dynkin EB. Markov processes. Vol. I. Springer-Verlag, 1965

Vol. 24 No. 2 (2019)