𝕃²-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration

References

[1] K. Bahlali, Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient, Electron. Commun. Probab. 7 (2002), 169–179. 10.1214/ECP.v7-1058Search in Google Scholar

[2] K. Bahlali, M. Eddahbi and E. Essaky, BSDE associated with Lévy processes and application to PDIE, J. Appl. Math. Stochastic Anal. 16 (2003), no. 1, 1–17. 10.1155/S1048953303000017Search in Google Scholar

[3] K. Bahlali, E. Essaky and M. Hassani, Multidimensional BSDEs with super-linear growth coefficient: Application to degenerate systems of semilinear PDEs, C. R. Math. Acad. Sci. Paris 348 (2010), no. 11–12, 677–682. 10.1016/j.crma.2010.03.006Search in Google Scholar

[4] K. Bahlali, E. Essaky and M. Hassani, Existence and uniqueness of multidimensional BSDEs and of systems of degenerate PDEs with superlinear growth generator, SIAM J. Math. Anal. 47 (2015), no. 6, 4251–4288. 10.1137/130947933Search in Google Scholar

[5] K. Bahlali, E. H. Essaky, M. Hassani and E. Pardoux, Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient, C. R. Math. Acad. Sci. Paris 335 (2002), no. 9, 757–762. 10.1016/S1631-073X(02)02542-6Search in Google Scholar

[6] D. Becherer, M. Büttner and K. Kentia, On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples, Frontiers in Stochastic Analysis—BSDEs, SPDEs and Their Applications, Springer Proc. Math. Stat. 289, Springer, Cham (2019), 1–41. 10.1007/978-3-030-22285-7_1Search in Google Scholar

[7] I. Bihari, A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Acad. Sci. Hungar. 7 (1956), 81–94. 10.1007/BF02022967Search in Google Scholar

[8] J.-M. Bismut, Théorie probabiliste du contrôle des diffusions, Mem. Amer. Math. Soc. 167 (1976), 1–130. 10.1090/memo/0167Search in Google Scholar

[9] P. Briand, B. Delyon, Y. Hu, E. Pardoux and L. Stoica, L p solutions of backward stochastic differential equations, Stochastic Process. Appl. 108 (2003), no. 1, 109–129. 10.1016/S0304-4149(03)00089-9Search in Google Scholar

[10] M. Eddahbi, I. Fakhouri and Y. Ouknine, 𝕃 p ( p ≥ 2 ) -solutions of generalized BSDEs with jumps and monotone generator in a general filtration, Mod. Stoch. Theory Appl. 4 (2017), no. 1, 25–63. 10.15559/17-VMSTA73Search in Google Scholar

[11] S. Fan, L p solutions of multidimensional BSDEs with weak monotonicity and general growth generators, J. Math. Anal. Appl. 432 (2015), no. 1, 156–178. 10.1016/j.jmaa.2015.06.049Search in Google Scholar

[12] C. Geiss and A. Steinicke, Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting, Probab. Uncertain. Quant. Risk 3 (2018), Paper No. 9. 10.1186/s41546-018-0034-ySearch in Google Scholar PubMed PubMed Central

[13] S. Hamadene, Équations différentielles stochastiques rétrogrades: les cas localement lipschitzien, Ann. Inst. Henri Poincaré Probab. Stat. 32 (1996), no. 5, 645–659. Search in Google Scholar

[14] J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, 2nd ed., Grundlehren Math. Wiss. 288, Springer, Berlin, 2003. 10.1007/978-3-662-05265-5Search in Google Scholar

[15] T. Klimsiak and A. Rozkosz, Obstacle problem for semilinear parabolic equations with measure data, J. Evol. Equ. 15 (2015), no. 2, 457–491. 10.1007/s00028-014-0269-8Search in Google Scholar

[16] T. Klimsiak and A. Rozkosz, Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms, Colloq. Math. 145 (2016), no. 1, 35–67. 10.4064/cm6466-10-2015Search in Google Scholar

[17] T. Kruse and A. Popier, BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration, Stochastics 88 (2016), no. 4, 491–539. 10.1080/17442508.2015.1090990Search in Google Scholar

[18] J. LaSalle, Uniqueness theorems and successive approximations, Ann. of Math. (2) 50 (1949), 722–730. 10.2307/1969559Search in Google Scholar

[19] X. Mao, Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Process. Appl. 58 (1995), no. 2, 281–292. 10.1016/0304-4149(95)00024-2Search in Google Scholar

[20] D. Nualart and W. Schoutens, Backward stochastic differential equations and Feynman–Kac formula for Lévy processes, with applications in finance, Bernoulli 7 (2001), no. 5, 761–776. 10.2307/3318541Search in Google Scholar

[21] E. Pardoux, BSDEs, weak convergence and homogenization of semilinear PDEs, Nonlinear Analysis, Differential Equations and Control (Montreal 1998), NATO Sci. Ser. C Math. Phys. Sci. 528, Kluwer Academic, Dordrecht (1999), 503–549. 10.1007/978-94-011-4560-2_9Search in Google Scholar

[22] E. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), no. 1, 55–61. 10.1016/0167-6911(90)90082-6Search in Google Scholar

[23] S. Rong, On solutions of backward stochastic differential equations with jumps and applications, Stochastic Process. Appl. 66 (1997), no. 2, 209–236. 10.1016/S0304-4149(96)00120-2Search in Google Scholar

[24] S. J. Tang and X. J. Li, Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim. 32 (1994), no. 5, 1447–1475. 10.1137/S0363012992233858Search in Google Scholar

[25] S.-Y. Xu and S.-J. Fan, A general existence and uniqueness result on multidimensional BSDEs, J. East China Norm. Univ. Natur. Sci. Ed. (2015), no. 1, 51–60. Search in Google Scholar

[26] S. Yao, 𝕃 p solutions of backward stochastic differential equations with jumps, Stochastic Process. Appl. 127 (2017), no. 11, 3465–3511. 10.1016/j.spa.2017.03.005Search in Google Scholar

[27] J. Yin and X. Mao, The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications, J. Math. Anal. Appl. 346 (2008), no. 2, 345–358. 10.1016/j.jmaa.2008.05.072Search in Google Scholar