Y. F. Atchade, G. Fort, and E. Moulines, On stochastic proximal gradient algorithms. ArXiv e-prints, 1402, p.2365, 2014.

H. Attouch, Familles d'op??rateurs maximaux monotones et mesurabilit??, Annali di Matematica Pura ed Applicata, Series 4, vol.276, issue.1, pp.35-111, 1979.
DOI : 10.2140/pjm.1968.24.525

J. Aubin and A. Cellina, Differential inclusions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, vol.264, 1984.
URL : https://hal.archives-ouvertes.fr/hal-00915425

H. H. Bauschke and J. M. Borwein, Legendre functions and the method of random bregman projections, Journal of Convex Analysis, vol.4, issue.1, pp.27-67, 1997.

H. H. Bauschke, J. M. Borwein, and W. Li, Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization, Mathematical Programming, pp.135-160, 1999.
DOI : 10.1007/s101070050083

H. H. Bauschke and P. L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces, CMS Books in Mathematics, 2011.
DOI : 10.1007/978-3-319-48311-5

URL : https://hal.archives-ouvertes.fr/hal-00643354

M. Bena¨?mbena¨?m, Dynamics of stochastic approximation algorithms, Séminaire de Probabilités, XXXIII, pp.1-68, 1999.

M. Bena¨?mbena¨?m and M. W. Hirsch, Stochastic approximation algorithms with constant step size whose average is cooperative, Ann. Appl. Probab, vol.9, issue.1, pp.216-241, 1999.

M. Bena¨?mbena¨?m, J. Hofbauer, and S. Sorin, Stochastic Approximations and Differential Inclusions, SIAM Journal on Control and Optimization, vol.44, issue.1, pp.328-348, 2005.
DOI : 10.1137/S0363012904439301

D. P. Bertsekas, Incremental proximal methods for large scale convex optimization, Mathematical Programming, vol.8, issue.2, pp.163-195, 2011.
DOI : 10.1137/S1052623495294797

URL : http://www-mit.mit.edu/dimitrib/www/Incremental_Proximal.pdf

P. Bianchi, Ergodic Convergence of a Stochastic Proximal Point Algorithm, SIAM Journal on Optimization, vol.26, issue.4, pp.2235-2260, 2016.
DOI : 10.1137/15M1017909

P. Bianchi and W. Hachem, Dynamical Behavior of a Stochastic Forward???Backward Algorithm Using Random Monotone Operators, Journal of Optimization Theory and Applications, vol.7, issue.3, pp.90-120, 2016.
DOI : 10.1080/17442508208833217

URL : https://hal.archives-ouvertes.fr/hal-01183959

P. Bianchi, W. Hachem, and A. Salim, Constant step stochastic approximations involving differential inclusions: Stability, long-run convergence and applications. arXiv preprint, 2016.

J. M. Borwein and A. S. Lewis, Convex analysis and nonlinear optimization, CMS Books in Mathematics, vol.3

H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland mathematics studies, 1973.

R. E. Bruck and J. , Asymptotic convergence of nonlinear contraction semigroups in Hilbert space, Journal of Functional Analysis, vol.18, issue.1, pp.15-26, 1975.
DOI : 10.1016/0022-1236(75)90027-0

C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, vol.580, 1977.
DOI : 10.1007/BFb0087685

P. L. Combettes and J. Pesquet, Stochastic Quasi-Fej??r Block-Coordinate Fixed Point Iterations with Random Sweeping, SIAM Journal on Optimization, vol.25, issue.2, pp.1221-1248, 2015.
DOI : 10.1137/140971233

URL : http://arxiv.org/pdf/1404.7536

P. L. Combettes and J. Pesquet, Stochastic approximations and perturbations in forwardbackward splitting for monotone operators, Pure Appl. Funct. Anal, vol.1, issue.1, pp.13-37, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01380000

J. De-vries, Elements of topological dynamics, of Mathematics and its Applications, 1993.
DOI : 10.1007/978-94-015-8171-4

A. Dieuleveut, A. Durmus, and F. Bach, Bridging the gap between constant step size stochastic gradient descent and markov chains, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01565514

M. Faure and G. Roth, Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor, Mathematics of Operations Research, vol.35, issue.3, pp.624-640, 2010.
DOI : 10.1287/moor.1100.0455

URL : https://hal.archives-ouvertes.fr/hal-00383277

J. Fort and G. Pagès, Asymptotic Behavior of a Markovian Stochastic Algorithm with Constant Step, SIAM Journal on Control and Optimization, vol.37, issue.5, pp.1456-1482, 1999.
DOI : 10.1137/S0363012997328610

F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, Journal of Multivariate Analysis, vol.7, issue.1, pp.149-182, 1977.
DOI : 10.1016/0047-259X(77)90037-9

J. Hiriart-urruty, About properties of the mean value functional and of the continuous infimal convolution in stochastic convex analysis, pp.763-789, 1976.

J. Hiriart-urruty, ContributionsàContributions`Contributionsà la programmation mathématique: cas déterministe et stochastique Université de Clermont-Ferrand II, Clermont-Ferrand, Thèse présentéè a l'Université de Clermont-Ferrand II pour obtenir le grade de DocteurèsDocteurès Sciences Mathématiques, 1977.

H. J. Kushner and G. G. Yin, Stochastic approximation and recursive algorithms and applications, Stochastic Modelling and Applied Probability, 2003.

P. Laurent, Approximation et optimisation, Collection Enseignement des Sciences, issue.13, 1972.

I. Molchanov, Theory of random sets. Probability and its Applications, 2005.
DOI : 10.1007/978-1-4471-7349-6

J. Neveu, Bases mathématiques du calcul des probabilités, Masson et Cie, ´ Editeurs, 1964.

J. Peypouquet and S. Sorin, Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time, J. Convex Anal, vol.17, pp.3-41113, 2010.

R. R. Phelps, Lectures on maximal monotone operators, Extracta Math, vol.12, issue.3, pp.193-230, 1997.

R. T. Rockafellar, Measurable dependence of convex sets and functions on parameters, Journal of Mathematical Analysis and Applications, vol.28, issue.1, pp.4-25, 1969.
DOI : 10.1016/0022-247X(69)90104-8

R. T. Rockafellar, Convex analysis. Princeton Mathematical Series, 1970.

R. T. Rockafellar and R. J. Wets, On the interchange of subdifferentiation and conditional expectation for convex functionals, Stochastics, vol.137, issue.3, pp.173-182, 1982.
DOI : 10.1007/BFb0120750

L. Rosasco, S. Villa, and B. C. V?uv?u, Convergence of stochastic proximal gradient algorithm, 2014.

L. Rosasco, S. Villa, and B. C. V?uv?u, A stochastic inertial forward?backward splitting algorithm for multivariate monotone inclusions. Optimization, pp.1293-1314, 2016.
DOI : 10.1080/02331934.2015.1127371

URL : http://arxiv.org/pdf/1507.00848

G. Roth and W. H. Sandholm, Stochastic Approximations with Constant Step Size and Differential Inclusions, SIAM Journal on Control and Optimization, vol.51, issue.1, pp.525-555, 2013.
DOI : 10.1137/110844192

D. W. Walkup and R. J. Wets, Stochastic Programs with Recourse II: On the Continuity of the Objective, SIAM Journal on Applied Mathematics, vol.17, issue.1, pp.98-103, 1969.
DOI : 10.1137/0117010