References
- E. Alos and D. Nualart, Stochastic integration with respect to the fractional Brownian motion, Stoch. Stoch. Rep. 75 (2003), no. 3, 129-152. https://doi.org/10.1080/1045112031000078917
- K. Bahlali, M. Eddahbi, and M. Mellouk, Stability and genericity for spde's driven by spatially correlated noise, J. Math. Kyoto Univ. 48 (2008), no. 4, 699-724. https://doi.org/10.1215/kjm/1250271314
- K. Bahlali, B. Mezerdi, and Y. Ouknine, Pathwise uniqueness and approximation of solutions of stochastic differential equations, in Seminaire de Probabilites, XXXII, 166-187, Lecture Notes in Math., 1686, Springer, Berlin, 1998.
- R. M. Balan and C. A. Tudor, Erratum to: "The stochastic heat equation with fractionalcolored noise: existence of the solution", ALEA Lat. Am. J. Probab. Math. Stat. 6 (2009), 343-347.
- V. Bally, I. Gyongy, and Pardoux, White noise driven parabolic SPDEs with measurable drift, J. Funct. Anal. 120 (1994), no. 2, 484-510. https://doi.org/10.1006/jfan.1994.1040
- V. Bally, A. Millet, and M. Sanz-Sole, Approximation and support theorem in Holder norm for parabolic stochastic partial differential equations, Ann. Probab. 23 (1995), no. 1, 178-222. https://doi.org/10.1214/aop/1176988383
- X. Bardina, M. Jolis, and L. Quer-Sardanyons, Weak convergence for the stochastic heat equation driven by Gaussian white noise, Electron. J. Probab. 15 (2010), no. 39, 1267-1295. https://doi.org/10.1214/EJP.v15-792
- R. Carmona and D. Nualart, Random nonlinear wave equations: smoothness of the solutions, Probab. Theory Related Fields 79 (1988), no. 4, 469-508. https://doi.org/10.1007/BF00318783
- E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill Book Company, Inc., New York, 1955.
- R. C. Dalang and M. Sanz-Sole, Regularity of the sample paths of a class of second-order spde's, J. Funct. Anal. 227 (2005), no. 2, 304-337. https://doi.org/10.1016/j.jfa.2004.11.015
- L. Decreusefond and A. S. Ustunel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (1999), no. 2, 177-214. https://doi.org/10.1023/A:1008634027843
- G. Denk, D. Meintrup, and S. Schaffer, Modeling, simulation and optimization of integrated circuits, Intern. Ser. Numerical Math. 146 (2004), 251-267.
- O. El Barrimi and Y. Ouknine, Approximation of solutions of SDEs driven by a fractional Brownian motion, under pathwise uniqueness, Mod. Stoch. Theory Appl. 3 (2016), no. 4, 303-313. https://doi.org/10.15559/16-VMSTA69
- M. Gubinelli, A. Lejay, and S. Tindel, Young integrals and SPDEs, Potential Anal. 25 (2006), no. 4, 307-326. https://doi.org/10.1007/s11118-006-9013-5
- I. Gyongy and D. Nualart, Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise, Potential Anal. 7 (1997), no. 4, 725-757. https://doi.org/10.1023/A:1017998901460
- S. C. Kou and X. Sunney, Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule, Phys. Rev. Letters 93 (2004), no. 18.
- B. B. Mandelbrot and J. W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968), 422-437. https://doi.org/10.1137/1010093
- J. Memin, Y. Mishura, and E. Valkeila, Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion, Statist. Probab. Lett. 51 (2001), no. 2, 197-206. https://doi.org/10.1016/S0167-7152(00)00157-7
- D. Nualart and Y. Ouknine, Regularization of quasilinear heat equations by a fractional noise, Stoch. Dyn. 4 (2004), no. 2, 201-221. https://doi.org/10.1142/S0219493704001012
- L. Quer-Sardanyons and S. Tindel, The 1-d stochastic wave equation driven by a fractional Brownian sheet, Stochastic Process. Appl. 117 (2007), no. 10, 1448-1472. https://doi.org/10.1016/j.spa.2007.01.009
- J. M. Rassias, Counterexamples in Differential Equations and Related Topics, World Scientific Publishing Co., Inc., Teaneck, NJ, 1991.
- A. V. Skorokhod, Studies in the Theory of Random Processes, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, MA, 1965.
- J. B. Walsh, An introduction to stochastic partial differential equations, in Ecole d'ete de probabilites de Saint-Flour, XIV-1984, 265-439, Lecture Notes in Math., 1180, Springer, Berlin, 1986.
- M. Yor, Le drap brownien comme limite en loi de temps locaux lineaires, in Seminar on probability, XVII, 89-105, Lecture Notes in Math., 986, Springer, Berlin, 1983.