ON INFINITESIMAL GENERATORS OF SUBLINEAR MARKOV SEMIGROUPS

[1] H. Airault and H. Fo¨llmer: Relative Densities of Semimartingales, Invent. Math. 27 (1974), 299–327.

[2] D. Applebaum and T. Le Ngan: The positive maximum principle on Lie groups, J. London Math. Soc. 101(2020), 136–155.

[3] G. Barles and C. Imbert: Second-order elliptic integro-differential equations: Viscosity solutions’ theory revisited, Ann. Inst. H. Poincare´ Anal Non Line´aure 25 (2008), 567–585.

[4] B. Bo¨ttcher, R. Schilling and J. Wag: Le´vy Matters, III: Le´vy-Type Processes: Construction, Approxima- tion and Sample Path Properties, Lecture Notes in Mathematics 2099, Springer, 2014.

[5] P. Courre`ge: Sur la forme inte´gro diffe´rentielle des ope´rateurs de C∞ dans C satisfaisant au principe du maximum; in Se´minaire de The´orie du Potentiel 10 (1965/66), expose´ 2, pp.1–38.

[6] M. Crandall and P. Lions: Viscosity solutions of Hamilton–Jacobi equations. Trans. Amer. Math. Soc. 277(1983), 1–42.

[7] R. Denk, M. Kupper and M. Nendel: A semigroup approach to nonlinear Le´vy processes, Stochastic Pro- cess Appl. 130 (2020), 1616–1642.

[8] R. Denk, M. Kupper and M. Nendel: Convex semigroups on Banach lattices, arXiv 1909.02281.

[9] E.B. Dynkin: Markov Processes I, Springer-Verlag, Berlin-Go¨ttingen-Heidellberg, 1965.

[10] L. Evans: On solving certain nonlinear partial differential equations by accretive operator methods, Israel J. Math. 36 (1980), 225–247.

[11] W. Hoh: Pseudo-Differential Operators Generating Markov Processes, Habilitationsschrift. Universita¨t Bielefeld, Bielefeld, 1998.

[12] J. Hollender: Le´vy-Type Processes under Uncertainty and Related Nonlocal Equations, CreateSpace Inde- pendent Publishing Platform, 2016.

[13] N. Jacob: Pseudo Differential Operators and Markov Processes I, II, III. Imperial College Press/World Scientific, London, 2001–2005.

[14] D. Khoshnevisan and R.L. Schilling: From Le´vy-Type Processes to Parabolic SPDEs, Birkha¨user/Springer, Cham, 2017.

[15] F. Ku¨hn: Le´vy-Type Processes: Moments, Construction and Heat Kernel Estimates, Springer Lecture Notes in Mathematics 2187 (vol.6 of the Le´vy Matters subseries), Springer, Cham, 2017.

[16] F. Ku¨hn: Viscosity solutions to Hamilton-Jacobi-Bellman equations associated with sublinear Le´vy(-type) processes, ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019), 531–559.

[17] I. Miyadera: Nonlinear semigroups, American Mathematical Society, Providence (RI), 1992.

[18] M. Nendel and M. Ro¨ckner: Upper envelopes of families of Feller semigroups and viscosity solutions to a class of nonlinear Cauchy problems, arXiv 1906.04430.

[19] S. Peng: G-expectation, G-Brownian motion and related stochastic calculus of Itoˆ type; in Stochastic Analysis and Applications, The Abel Symp. 2, Springer, Berlin, 2007, 541–567.

[20] R.L. Schilling: Conservativeness of semigroups generated by pseudo differential operators, Potential Anal.9 (1998), 91–104.

[21] A. Schnurr: On the semimartingale nature of Feller processes with killing, Stochastic. Process. Appl. 122(2012), 2758–2780.

[22] W. von Waldenfels: Eine Klasse stationa¨rer Markov prozesse, Kernforschungsanlage Ju¨lich, Institut fu¨r Plasma-physik, Ju¨lich, 1961.

[23] W. von Waldenfels: Fast positive Operatoren, Z. Wahrscheinlichkeitstheorie und Verw. Gebete 4 (1965), 159–174.