Open Access
Volume 29, 2023
Article Number 43
Number of page(s) 22
Published online 09 June 2023
  1. Y. Achdou and S. Patrizi, Homogenization of first-order equations with u/ϵ-periodic Hamiltonian: rate of convergence as ϵ → 0 and numerical methods. Math. Models Methods Appl. Sci. 21 (2011) 1317–1353. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Arisawa, Homogenizations of integro-differential equations with Lévy operators with asymmetric and degenerate densities. Proc. Roy. Soc. Edinb. Sect. A 142 (2012) 917–943. [CrossRef] [Google Scholar]
  3. M. Bardi, A. Cesaroni and E. Topp, Cauchy problem and periodic homogenization for nonlocal Hamilton–Jacobi equations with coercive gradient terms. Proc. Roy. Soc. Edinb. Sect. A 150 (2020) 3028–3059. [CrossRef] [Google Scholar]
  4. M. Bardi and G. Terrone, Periodic homogenization of deterministic control problems via limit occupational measures, in Dynamics, Games and Science, Vol. 1 of CIM Ser. Math. Sci. Springer, Cham (2015) 105–116. [CrossRef] [Google Scholar]
  5. G. Barles, E. Chasseigne, A. Ciomaga and C. Imbert, Lipschitz regularity of solutions for mixed integro-differential equations. J. Diff. Equ. 252 (2012) 6012–6060. [CrossRef] [Google Scholar]
  6. G. Barles, E. Chasseigne, A. Ciomaga and C. Imbert, Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations. Calc. Var. Partial Diff. Equ. 50 (2022) 283–304. [Google Scholar]
  7. G. Barles and C. Imbert, Second-order elliptic integro-differential equations: viscosity solutions’ theory revisited, Ann. Institut Henri Poincare (C) Non Linear Anal. 25 (2208) 567–585. [Google Scholar]
  8. G. Barles, O. Ley and E. Topp, Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior. Nonlinearity 30 (2017) 703–734. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equations. Commun.Pure Appl. Math. 62 (2009) 597–638. [CrossRef] [Google Scholar]
  10. F. Camilli and C. Marchi, Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs. Nonlinearity 22 (2009) 1481–1498. [CrossRef] [MathSciNet] [Google Scholar]
  11. I Capuzzo-Dolcetta and H Ishii, On the rate of convergence in homogenization of Hamilton-Jacobi equations. Indiana Univ. Math. J. 50 (2001) 1113–1129. [CrossRef] [Google Scholar]
  12. H. Chang-Lara and G. Davila, Holder estimates for non-local parabolic equations with critical drift. J. Diff. Equ. 260 (2016) 4237–4284. [CrossRef] [Google Scholar]
  13. A. Ciomaga, D. Ghilli and E. Topp, Periodic homogenization for weakly elliptic Hamilton–Jacobi–Bellman equations with critical fractional diffusion. Commun. Partial Diff. Equ. 47 (2022) 1–38. [CrossRef] [Google Scholar]
  14. R. Cont and P. Tankov, Financial Modelling with Jump Processes. Chapman & Hall/CRC (2003). [Google Scholar]
  15. Ph. Courrege, Sur la forme intégro-différentielle des opérateurs de ck dans c satisfaisant au principe du maximum. Sémin. Brelot-Choquet-Deny. Théorie Potentiel. 10 (1965) 1–38. [Google Scholar]
  16. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  17. L.C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Roy. Soc. Edinb. Sect. A: Math. 111 (1989) 359–375. [CrossRef] [Google Scholar]
  18. L.C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations. Proc. Roy. Soc. Edinb. Sect. A: Math. 120 (1992) 245–265. [CrossRef] [Google Scholar]
  19. N. Guillen, C. Mou and A. Świȩch, Coupling Lévy measures and comparison principles for viscosity solutions. Trans. Amer. Math. Soc. 372 (2019) 7327–7370. [CrossRef] [MathSciNet] [Google Scholar]
  20. N. Guillen and R.W. Schwab, Min–max formulas for nonlocal elliptic operators. Calc. Var. Partial Diff. Equ. 58 (2019) 1–79. [CrossRef] [Google Scholar]
  21. H. Ishii, H. Mitake and H.V. Tran, The vanishing discount problem and viscosity Mather measures. Part 1: The problem on a torus. J. Math. Pures Appl. 108 (2017) 125–149. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Kassmann, A. Piatnitski and E. Zhizhina, Homogenization of Lévy-type operators with oscillating coefficients. SIAM J. Math. Anal. 51 3641–3665. [Google Scholar]
  23. S. Kim and K.-A. Lee, Higher order convergence rates in theory of homogenization: equations of non-divergence form. Arch. Rational Mech. Anal. 219 (2016) 1273–1304. [CrossRef] [MathSciNet] [Google Scholar]
  24. B. Øksendal and A. Sulem, Applied Stochastic Control of Jump Diffusions. Universitext. Springer, Cham (2019). [CrossRef] [Google Scholar]
  25. H. Mitake, H.V. Tran and Y. Yu, Rate of convergence in periodic homogenization of Hamilton-–Jacobi equations: the convex setting. Arch. Rational Mech. Anal. 233 (2019) 901–934. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Mou and A. Świech, Uniqueness of viscosity solutions for a class of integro-differential equations. Nonlinear Diff. Equ. Applic. NoDEA. 22 1851–1882. [Google Scholar]
  27. G. Papanicolaou, P.L. Lions and S.R.S. Varadhan, Homogeneization of Hamilton–Jacobi equations. Unpublished, 1986. [Google Scholar]
  28. H. Pham, Optimal stopping of controlled jump diffusion processes: a viscosity solution approach. J. Math. Syst. Estim. Control 8 (1998) 1–27. [Google Scholar]
  29. A. Piatnitski and E. Zhizhina, Periodic homogenization of nonlocal operators with a convolution-type kernel. SIAM J. Math. Anal. 49 (2017) 64–81. [CrossRef] [MathSciNet] [Google Scholar]
  30. R.W. Schwab, Periodic homogenization for nonlinear integro-differential equations. SIAM J. Math. Anal. 42 (2010) 2652–2680. [CrossRef] [MathSciNet] [Google Scholar]
  31. J. Serra, Cσ+α regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels. Calc. Var. Partial Diff. Equ. 54 (2015) 3571–3601. [CrossRef] [Google Scholar]
  32. M. Sion, On general minimax theorems. Pacific J. Math. 8 (1958) 171–176. [CrossRef] [MathSciNet] [Google Scholar]
  33. T. Tabet Tchamba, Large time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian. Asymptotic Anal. 66 (2010) 161–186. [CrossRef] [MathSciNet] [Google Scholar]
  34. G. Terrone, Limiting relaxed controls and averaging of singularly perturbed deterministic control systems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 18 (2011) 653–672. [MathSciNet] [Google Scholar]

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