Stability results for stochastic differential equations driven by an additive fractional Brownian sheet

References

[1] E. Alòs, O. Mazet and D. Nualart, Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1 2 , Stochastic Process. Appl. 86 (2000), no. 1, 121–139. 10.1016/S0304-4149(99)00089-7Search in Google Scholar

[2] E. Alòs, O. Mazet and D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab. 29 (2001), no. 2, 766–801. 10.1214/aop/1008956692Search in Google Scholar

[3] A. Ayache, S. Leger and M. Pontier, Drap brownien fractionnaire, Potential Anal. 17 (2002), no. 1, 31–43. 10.1023/A:1015260803576Search in Google Scholar

[4] 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. 10.1215/kjm/1250271314Search in Google Scholar

[5] K. Bahlali, B. Mezerdi and Y. Ouknine, Pathwise uniqueness and approximation of solutions of stochastic differential equations, Séminaire de Probabilités XXXII, Lecture Notes in Math. 1686, Springer, Berlin (1998), 166–187. 10.1007/BFb0101757Search in Google Scholar

[6] X. Bardina, M. Jolis and C. A. Tudor, Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes, Statist. Probab. Lett. 65 (2003), no. 4, 317–329. 10.1016/j.spl.2003.09.001Search in Google Scholar

[7] P. J. Bickel and M. J. Wichura, Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Statist. 42 (1971), 1656–1670. 10.1214/aoms/1177693164Search in Google Scholar

[8] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. Search in Google Scholar

[9] L. Decreusefond and A. S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (1999), no. 2, 177–214. 10.1023/A:1008634027843Search in Google Scholar

[10] O. El Barrimi and Y. Ouknine, Some stability results for semilinear stochastic heat equation driven by a fractional noise, Bull. Korean Math. Soc. 56 (2019), no. 3, 631–648. Search in Google Scholar

[11] O. El Barrimi and Y. Ouknine, Stochastic differential equations driven by an additive fractional Brownian sheet, Bull. Korean Math. Soc. 56 (2019), no. 2, 479–489. Search in Google Scholar

[12] M. Erraoui, Y. Ouknine and D. Nualart, Hyperbolic stochastic partial differential equations with additive fractional Brownian sheet, Stoch. Dyn. 3 (2003), no. 2, 121–139. 10.1142/S0219493703000681Search in Google Scholar

[13] Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions, Mem. Amer. Math. Soc. 175 (2005), no. 825, 1–127. 10.1090/memo/0825Search in Google Scholar

[14] A. Kamont, On the fractional anisotropic Wiener field, Probab. Math. Statist. 16 (1996), no. 1, 85–98. Search in Google Scholar

[15] S. Léger and M. Pontier, Drap brownien fractionnaire, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 10, 893–898. 10.1016/S0764-4442(00)87495-9Search in Google Scholar

[16] Y. S. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lecture Notes in Math. 1929, Springer, Berlin, 2008. 10.1007/978-3-540-75873-0Search in Google Scholar

[17] D. Nualart, Stochastic integration with respect to fractional Brownian motion and applications, Stochastic Models, Contemp. Math. 336, American Mathematical Society, Providence (2003), 3–39. 10.1090/conm/336/06025Search in Google Scholar

[18] D. Nualart, The Malliavin Calculus and Related Topics, 2nd ed., Probab. Appl. (New York), Springer, Berlin, 2006. Search in Google Scholar

[19] J. M. Rassias, Counterexamples in Differential Equations and Related Topics, World Scientific, Teaneck, 1991. 10.1142/1258Search in Google Scholar

[20] T. Sottinen and C. A. Tudor, On the equivalence of multiparameter Gaussian processes, J. Theoret. Probab. 19 (2006), no. 2, 461–485. 10.1007/s10959-006-0022-5Search in Google Scholar