[1] Benaïm M, Ledoux M, Raimond O. Self-interacting diffusions. Prob Theory Rel Fields, 2002, 122: 1-41 [2] Benaïm M, Ciotir I, Gauthier C E. Self-repelling diffusions via an infinite dimensional approach. Stoch PDE: Anal Comp, 2015, 3: 506-530 [3] Bertoin J. Sur une intégrale pour les processus á $\alpha$-variation borné. Ann Probab, 1989 17: 1521-1535 [4] Biagini F, Hu Y, Øksendal B, Zhang T.Stochastic Calculus for fBm and Applications. Berlin: Springer, 2008 [5] Cranston M, Le Jan Y. Self-attracting diffusions: Two case studies. Math Ann, 1995, 303: 87-93 [6] Cranston M, Mountford T S. The strong law of large numbers for a Brownian polymer. Ann Probab, 1996, 24: 1300-1323 [7] Durrett R, Rogers L C G. Asymptotic behavior of Brownian polymer. Prob Theory Rel Fields, 1991, 92: 337-349 [8] FöIllmer H. Calcul d'Itô sans probabilités//Azéme J, Yor M. Séinaire de Probabilités XV.1980, 50: 143-145 [9] Gan Y, Yan L.Least squares estimation for the linear self-repelling diffusion driven by fractional Brownian motion (in Chinese). Sci China Math, 2018, 48: 1143-1158 [10] Gauthier C E. Self attracting diffusions on a sphere and application to a periodic case. Electron Commun Probab, 2016, 21: Art 53 [11] Herrmann S, Roynette B. Boundedness and convergence of some self-attracting diffusions. Math Ann, 2003, 325: 81-96 [12] Herrmann S, Scheutzow M. Rate of convergence of some self-attracting diffusions. Stochastic Process Appl, 2004, 111: 41-55 [13] Hu Y. Integral transformations and anticipative calculus for fBms. Memoirs Amer Math Soc, 2005, 175: Art 825 [14] Mishura Y.Stochastic Calculus for fBm and Related Processes. Berlin: Springer, 2008 [15] Mountford T, Tarrés P. An asymptotic result for Brownian polymers. Ann Inst H Poincare Probab Statist, 2008, 44: 29-46 [16] Nourdin I.Selected Aspects of Fractional Brownian Motion. Berlin: Springer, 2012 [17] Nualart D.Malliavin Calculus and Related Topics. Berlin: Springer-Verlag, 2006 [18] Pipiras V, Taqqu M. Integration questions related to the fractional Brownian motion. Probab Theory Related Fields, 2001, 118: 251-281 [19] Sun X, Yan L, Ge Y. The laws of large numbers associated with the linear self-attracting diffusion driven by fractional Brownian motion and applications. Journal of Theoretical Probability, 2022, 35: 1423-1478 [20] Tudor Ciprian A.Analysis of Variations for Self-Similar Processes. Berlin: Springer-Verlag, 2013 [21] Yan L, Sun Y, Lu Y. On the linear fractional self-attracting diffusion. J Theort Probab, 2008, 21: 502-516 |