Reflecting image-dependent SDEs in Wasserstein space and large deviation principle

References

• D. Adams, G. dos Reis, R. Ravaille, W. Salkeld, and J. Tugaut, Large deviations and exit-times for reflected McKean–Vlasov equations with self-stabilizing terms and superlinear drifts, Stoch. Proc. Appl. 146 (2022), pp. 264–310.
   Web of Science ®Google Scholar
• M. Boue and P. Dupuis, A variational representation for certain functionals of Brownian motion, Ann. Probab. 26 (1998), pp. 1641–1659.
   Web of Science ®Google Scholar
• P. Briand, P. Cardaliaguet, P-E. Chaudru de Raynal, and Y. Hu, Forward and backward stochastic differential equations with normal constraint in law, Stoch. Proc. Appl. 130 (2020), pp. 7021–7097.
   Web of Science ®Google Scholar
• P. Briand, R. Elie, and Y. Hu, BSDEs with mean reflexion, Ann. Appl. Probab. 28 (2018), pp. 482–510.
   Web of Science ®Google Scholar
• P. Briand, A. Ghannoum, and C. Labart, Mean reflected stochastic differential equations with jumps, Adv. Appl. Probab. 52 (2020), pp. 523–562.
   Web of Science ®Google Scholar
• A. Budhiraja and P. Dupuis, A variational representation for positive functionals of infinite dimensional Brownian motion, Probab. Math. Statist. 20 (2000), pp. 39–61.
   Google Scholar
• A. Budhiraja, P. Dupuis, and V. Maroulas, Large deviations for infinite dimensional stochastic dynamical systems continuous time processes, Ann. Probab. 36 (2008), pp. 1390–1420.
   Web of Science ®Google Scholar
• P. Cardaliaguet, F. Delarue, J.-M. Lasry, and P.-L. Lions, The Master Equation and the Convergence Problem in Mean Field Games Vol. 381, Princeton University Press, 2019. AMS-201,9780691190709. hal-01196045 .
   Google Scholar
• R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications II, Mean-field Games with Common Noise and Master Equations, Springer, 2018.
   Google Scholar
• R. Carmona, F. Delarue, and F. Lacker, Mean field games with common noise, Ann. Probab. 44 (2016), pp. 3740–3803.
   Web of Science ®Google Scholar
• F. Delarue, D. Lacker, and K. Ramanan, From the master equation to mean field game limit theory: A central limit theorem, Electron. J. Probab. 24 (2019), pp. 1–54.
   Web of Science ®Google Scholar
• G. dos Reis, W. Salkeld, and J. Tugaut, Freidlin-wentzell LDPs in path space for McKean–Vlasov equations and the functional iterated logarithm law, Ann. Appl. Probab. 29 (2019), pp. 1487–1540.
   Web of Science ®Google Scholar
• P. Chow, Large deviation problem for some parabolic itô equations, Commun. Pure Appl. Math. 45 (1992), pp. 97–120.
   Web of Science ®Google Scholar
• A. Gégout-Petit and E. Pardoux, Équations différentielles stochastiques rétrogrades réfléchies dans un convexe, Stoch. Stoch. Rep. 57 (1996), pp. 111–128.
   Google Scholar
• S. Herrmann, P. Imkeller, and D. Peithmann, Large deviations and a Kramers' type law for self-stabilizing diffusions, Ann. Appl. Probab. 18 (2008), pp. 1379–1423.
   Web of Science ®Google Scholar
• P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984), pp. 511–537.
   Web of Science ®Google Scholar
• W. Liu, Large deviations for stochastic evolution equations with small multiplicative noise, Appl. Math. Opt. 61 (2010), pp. 27–56.
   Web of Science ®Google Scholar
• W. Liu, Y. Song, J. Zhai, and T. Zhang, Large and moderate deviation principles for McKean–Vlasov SDEs with jumps, Potential Anal.2022. https://doi.org/10.1007/s11118-022-10005-0
   Web of Science ®Google Scholar
• W. Liu and L. Wu, Large deviations for empirical measures of mean-field gibbs measures, Stoch. Proc. Appl. 130 (2020), pp. 503–520.
   Web of Science ®Google Scholar
• A. Matoussi, W. Sabbagh, and T. Zhang, Backward doubly SDEs and semilinear stochastic PDEs in a convex domain, Stoch. Proc. Appl. 127 (2017), pp. 2781–2815.
   Web of Science ®Google Scholar
• A. Matoussi, W. Sabbagh, and T. Zhang, Large deviation principles of obstacle problems for quasilinear stochastic PDEs, Appl. Math. Opt. 83 (2021), pp. 849–879.
   Web of Science ®Google Scholar
• J. Menaldi, Stochastic variational inequality for reflected diffusion, Indiana Univ. Math. J. 32 (1983), pp. 733–744.
   Web of Science ®Google Scholar
• D. Nualart and E. Pardoux, White noise driven quasilinear SPDEs with reflection, Probab. Theory Relat. Fields 93 (1992), pp. 77–89.
   Web of Science ®Google Scholar
• R. Pettersson, Penalization schemes for reflecting stochastic differential equations, Bernoulli 3 (1997), pp. 203–414.
   Web of Science ®Google Scholar
• P. Protter, Stochastic Integration and Differential Equations, Springer, Berlin, Heidelberg, 1990.
   Google Scholar
• P. Ren and F.-Y. Wang, Bismut formula for Lions derivative of distribution dependent SDEs and applications, J. Differ. Equ. 267 (2019), pp. 4745–4777.
   Web of Science ®Google Scholar
• M. Röckner, T. Zhang, and X. Zhang, Large deviations for stochastic tamed 3D Navier–Stokes equations, Appl. Math. Opt. 61 (2010), pp. 267–285.
   Web of Science ®Google Scholar
• H. Tanaka, Stochastic differential equations with reflecting boundary condition in convex regions, Hiroshima Math. J. 9 (1979), pp. 163–177.
   Google Scholar
• F.-Y. Wang, Image-dependent conditional McKean–Vlasov SDEs for measure-valued diffusion processes, J. Evol. Equ. 21 (2021), pp. 2009–2045.
   Web of Science ®Google Scholar
• T. Zhang, Systems of stochastic partial differential equations with reflection: Existence and uniqueness, Stoch. Proc. Appl. 121 (2011), pp. 1356–1372.
   Web of Science ®Google Scholar