Modern Stochastics: Theory and Applications

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Bass, R.F., Chen, Z.-Q.: Brownian motion with singular drift. Ann. Probab. 31(2), 791–817 (2003). MR1964949. https://doi.org/10.1214/aop/1048516536

Blei, S., Engelbert, H.J.: One-dimensional stochastic differential equations with generalized and singular drift. Stoch. Process. Appl. 123(12), 4337–4372 (2013). MR3096356. https://doi.org/10.1016/j.spa.2013.06.014

Brox, Th.: A one-dimensional diffusion process in a Wiener medium. Ann. Probab. 14(4), 1206–1218 (1986). MR0866343

Cannizzaro, G., Chouk, K.: Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential. Ann. Probab. 46(3), 1710–1763 (2018). 05. MR3785598. https://doi.org/10.1214/17-AOP1213

Castrequini, R.A., Russo, F.: Path dependent equations driven by Hölder processes. Stoch. Anal. Appl. 37(3), 480–498 (2019). MR3946622. https://doi.org/10.1080/07362994.2019.1585263

Delarue, F., Diel, R.: Rough paths and 1d SDE with a time dependent distributional drift: application to polymers. Probab. Theory Relat. Fields 165, 1–63 (2016). MR3500267. https://doi.org/10.1007/s00440-015-0626-8

Dereudre, D., Roelly, S.: Path-dependent infinite-dimensional SDE with non-regular drift: An existence result. Ann. Inst. Henri Poincaré Probab. Stat. 53(2), 641–657 (2017). MR3634268. https://doi.org/10.1214/15-AIHP728

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Engelbert, H.-J., Wolf, J.: Strong Markov local Dirichlet processes and stochastic differential equations. Teor. Veroâtn. Primen. 43(2), 331–348 (1998). MR1679006. https://doi.org/10.4213/tvp1468

Flandoli, F., Issoglio, E., Russo, F.: Multidimensional SDEs with distributional coefficients. Trans. Am. Math. Soc. 369, 1665–1688 (2017). MR3581216. https://doi.org/10.1090/tran/6729

Flandoli, F., Russo, F., Wolf, J.: Some SDEs with distributional drift. I. General calculus. Osaka J. Math. 40(2), 493–542 (2003). MR1988703

Flandoli, F., Russo, F., Wolf, J.: Some SDEs with distributional drift. II. Lyons-Zheng structure, Itô’s formula and semimartingale characterization. Random Oper. Stoch. Equ. 12(2), 145–184 (2004). MR2065168. https://doi.org/10.1163/156939704323074700

Frikha, N., Li, L.: Weak uniqueness and density estimates for SDEs with coefficients depending on some path-functionals. ArXiv preprint (2019). 1707.01295. MR4076774. https://doi.org/10.1214/19-AIHP992

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Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus, 2nd edn. Graduate Texts in Mathematics, vol. 113. Springer, New York (1991). MR1121940. https://doi.org/10.1007/978-1-4612-0949-2

Mohammed, S-E.A.: Stochastic functional differential equations, vol. 99. Pitman Advanced Publishing Program (1984). MR0754561

Ohashi, A., Russo, F., Teixeira, A.: SDEs for Bessel processes in low dimension and path-dependent extensions (2020). Preprint.

Portenko, N.I.: Generalized diffusion processes. Translations of Mathematical Monographs, vol. 83. American Mathematical Society, Providence, RI (1990). Translated from the Russian by H. H. McFaden. MR1104660. https://doi.org/10.1090/mmono/083

Rogers, L.C.G., Williams, D.: Diffusions, Markov processes, and Martingales. Cambridge University Press (2000). MR1780932. https://doi.org/10.1017/CBO9781107590120

Russo, F., Trutnau, G.: About a construction and some analysis of time inhomogeneous diffusions on monotonely moving domains. J. Funct. Anal. 221(1), 37–82 (2005). MR2124897. https://doi.org/10.1016/j.jfa.2004.08.007

Russo, F., Trutnau, G.: Some parabolic PDEs whose drift is an irregular random noise in space. Ann. Probab. 35(6), 2213–2262 (2007). MR2353387. https://doi.org/10.1214/009117906000001178

Russo, F., Vallois, P.: The generalized covariation process and Itô formula. Stoch. Process. Appl. 59(1), 81–104 (1995). MR1350257. https://doi.org/10.1016/0304-4149(95)93237-A

Scheutzow, M.: Stochastic delay equations. Lecture Notes, CIMPA School (2018)

Seignourel, P.: Discrete schemes for processes in random media. Probab. Theory Relat. Fields 118(3), 293–322 (2000). MR1800534. https://doi.org/10.1007/PL00008743

Stroock, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Classics in Mathematics. Springer, Berlin (2006). Reprint of the 1997 edition. MR2190038

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