References
- R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968.
- A. Bonfiglioli, E. Lanconelli, and F. Uguzzoni, Stratified Lie Groups and Potential Theory for Their Sub-Laplacians, Springer Monographs in Mathematics, Springer, Berlin, 2007.
- M. Chaleyat-Maurel and J.F. Le Gall, Green function, capacity and sample path properties for a class of hypoelliptic diffusion processes, Probab. Theory Relat. Fields 83 (1989), pp. 219–264. doi: 10.1007/BF00333149
- C. Dellacherie and P.A. Meyer, Probabilities and Potential, North-Holland publishing company, Amsterdam, New York, Oxford, 1978.
- A. Dvoretzky, P. Erdös, and S. Kakutani, Double points of paths of brownian motion in n-space, Acta Sci. Math. Szeged 12 (1950), pp. 75–81.
- A. Dvoretzky, P. Erdös, and S. Kakutani, Multiple points of paths of Brownian motion in the plane, Bull. Res. Council Israel 3 (1954), pp. 364–371.
- S.N. Evans, Multiple points in the sample paths of a Lévy process, Probab. Theory. Relat. Fields. 76 (1987), pp. 359–367. doi: 10.1007/BF01297491
- P.J. Fitzsimmons and T.S. Salisbury, Capacity and energy for multiparameter Markov processes, Ann. L'I.H.P. Probab. Statist. 25 (1989), pp. 325–350.
- M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter GmbH & Co. KG, Berlin/New York, 2011.
- L. Hörmander and A. Melin, Free systems of vector fields, Ark. Mat. 16 (1978), pp. 83–88.
- K. Itô, Brownian motions in a Lie group, Proc. Jpn. Acad. 26 (1950), pp. 4–10.
- D. Khoshnevisan, Multiparameter Processes: an Introduction to Random Fields, Springer-Verlag, Inc, New York, 2002.
- S. Kusuoka and D. Stroock, Applications of the Malliavin calculus. III, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), pp. 391–442.
- J.F. Le Gall, Wiener sausage and self-intersection local times, J. Funct. Anal. 88 (1990), pp. 299–341.
- J.F. Le Gall, J.S. Rosen, and N.R. Shieh, Multiple points of Lévy processes, Ann. Probab. 17 (1989), pp. 503–515.
- A. Nagel, E.M. Stein, and S. Wainger, Balls and metrics defined by vector fields. I. Basic properties, Acta Math. 155 (1985), pp. 103–147. doi: 10.1007/BF02392539
- S.C. Port and C.J. Stone, Brownian Motion and Classical Potential Theory, Academic Press, New York, San Francisco, London, 1978.
- L.P. Rothschild and E.M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), pp. 247–320.
- A. Rudenko, Some uniform estimates for the transition density of a Brownian motion on a Carnot group and their application to local times, Theory Stoch. Proc. 19 (2014), pp. 62–90.
- A. Rudenko, Intersection local times in L2 for Markov processes, Theory Stoch. Proc. 24 (2019), pp. 64–95.
- A. Rudenko, An estimate for surface measure of small balls in Carnot groups, Osaka J. Math 57 (2020), pp. 425–450.
- N.T. Varopoulos, L. Saloff-Coste, and T. Coulhon, Analysis and Geometry on Groups, Cambridge Tracts in Mathematics Vol. 100, Cambridge University Press, Cambridge, 1992.