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  • Bal, Guillaume. Convergence to SPDEs in Stratonovich form. Comm. Math. Phys. 292 (2009), no. 2, 457--477. MR2544739
  • Bally, Vlad; Millet, Annie; Sanz-Solé, Marta. Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations. Ann. Probab. 23 (1995), no. 1, 178--222. MR1330767
  • Bardina, Xavier; Jolis, Maria; Quer-Sardanyons, Lluís. Weak convergence for the stochastic heat equation driven by Gaussian white noise. Electron. J. Probab. 15 (2010), no. 39, 1267--1295. MR2678391
  • Brézis, H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. (French) North-Holland Mathematics Studies, No. 5. Notas de Matemática (50). North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. vi+183 pp. MR0348562
  • Brzeźniak, Zdzisław; Flandoli, Franco. Almost sure approximation of Wong-Zakai type for stochastic partial differential equations. Stochastic Process. Appl. 55 (1995), no. 2, 329--358. MR1313027
  • Buckdahn, Rainer; Ma, Jin. Stochastic viscosity solutions for nonlinear stochastic partial differential equations. I. Stochastic Process. Appl. 93 (2001), no. 2, 181--204. MR1828772
  • Buckdahn, Rainer; Ma, Jin. Stochastic viscosity solutions for nonlinear stochastic partial differential equations. II. Stochastic Process. Appl. 93 (2001), no. 2, 205--228. MR1831830
  • Carmona, René A.; Fouque, Jean-Pierre. A diffusion approximation result for two parameter processes. Probab. Theory Related Fields 98 (1994), no. 3, 277--298. MR1262967
  • Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136
  • Deya, Aurélien. A discrete approach to rough parabolic equations. Electron. J. Probab. 16 (2011), no. 54, 1489--1518. MR2827468
  • Deya, A.; Gubinelli, M.; Tindel, S. Non-linear rough heat equations. Probab. Theory Related Fields 153 (2012), no. 1-2, 97--147. MR2925571
  • Florit, Carme; Nualart, David. Diffusion approximation for hyperbolic stochastic differential equations. Stochastic Process. Appl. 65 (1996), no. 1, 1--15. MR1422876
  • Friz, Peter K.; Victoir, Nicolas B. Multidimensional stochastic processes as rough paths. Theory and applications. Cambridge Studies in Advanced Mathematics, 120. Cambridge University Press, Cambridge, 2010. xiv+656 pp. ISBN: 978-0-521-87607-0 MR2604669
  • Griego, Richard J.; Heath, David; Ruiz-Moncayo, Alberto. Almost sure convergence of uniform transport processes to Brownian motion. Ann. Math. Statist. 42 1971 1129--1131. MR0278389
  • Gubinelli, M. Controlling rough paths. J. Funct. Anal. 216 (2004), no. 1, 86--140. MR2091358
  • Gubinelli, Massimiliano; Tindel, Samy. Rough evolution equations. Ann. Probab. 38 (2010), no. 1, 1--75. MR2599193
  • Hu, Yaozhong; Nualart, David. Stochastic heat equation driven by fractional noise and local time. Probab. Theory Related Fields 143 (2009), no. 1-2, 285--328. MR2449130
  • Kac, Mark. A stochastic model related to the telegrapher's equation. Reprinting of an article published in 1956. Papers arising from a Conference on Stochastic Differential Equations (Univ. Alberta, Edmonton, Alta., 1972). Rocky Mountain J. Math. 4 (1974), 497--509. MR0510166
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940
  • Manthey, Ralf. Weak convergence of solutions of the heat equation with Gaussian noise. Math. Nachr. 123 (1985), 157--168. MR0809342
  • Manthey, Ralf. Weak approximation of a nonlinear stochastic partial differential equation. Random partial differential equations (Oberwolfach, 1989), 139--148, Internat. Ser. Numer. Math., 102, Birkhäuser, Basel, 1991. MR1185745
  • Mörters, Peter; Peres, Yuval. Brownian motion. With an appendix by Oded Schramm and Wendelin Werner. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010. xii+403 pp. ISBN: 978-0-521-76018-8 MR2604525
  • Pazy, A. Semigroups of linear operators and applications to partial differential equations. Applied Mathematical Sciences, 44. Springer-Verlag, New York, 1983. viii+279 pp. ISBN: 0-387-90845-5 MR0710486
  • Pinsky, Mark. Differential equations with a small parameter and the central limit theorem for functions defined on a finite Markov chain. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 1968 101--111. MR0228067
  • Rosenthal, Haskell P. On the subspaces of $L^{p}$ $(p>2)$ spanned by sequences of independent random variables. Israel J. Math. 8 1970 273--303. MR0271721
  • Runst, Thomas; Sickel, Winfried. Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations. de Gruyter Series in Nonlinear Analysis and Applications, 3. Walter de Gruyter & Co., Berlin, 1996. x+547 pp. ISBN: 3-11-015113-8 MR1419319
  • Skorokhod, A. V. Studies in the theory of random processes. Translated from the Russian by Scripta Technica, Inc. Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965 viii+199 pp. MR0185620
  • Sussmann, Héctor J. On the gap between deterministic and stochastic ordinary differential equations. Ann. Probability 6 (1978), no. 1, 19--41. MR0461664
  • Tessitore, Gianmario; Zabczyk, Jerzy. Wong-Zakai approximations of stochastic evolution equations. J. Evol. Equ. 6 (2006), no. 4, 621--655. MR2267702
  • Tindel, Samy. Diffusion approximation for elliptic stochastic differential equations. Stochastic analysis and related topics, V (Silivri, 1994), 255--268, Progr. Probab., 38, Birkhäuser Boston, Boston, MA, 1996. MR1396335
  • Tindel, Samy. Stochastic parabolic equations with anticipative initial condition. Stochastics Stochastics Rep. 62 (1997), no. 1-2, 1--20. MR1489179
  • Walsh, John B. A stochastic model of neural response. Adv. in Appl. Probab. 13 (1981), no. 2, 231--281. MR0612203

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