References
- Zvonkin. A. K. (1974). A transformation of the phase space of a diffusion process that removes the drift. Mat. Sb. (N.S.), 93(135):129–149.
- Aryasova, O. , Pilipenko, A. (2012). On properties of a flow generated by an SDE with discontinuous drift. Electron. J. Probab . 17:1–20. DOI: 10.1214/EJP.v17-2138.
- Baños, D. R. , Ortiz-Latorre, S. , Pilipenko, A. , Proske, F. (2017) Strong solutions of SDE’s with generalized drift and multidimensional fractional Brownian initial noise. arXiv:1705.01616.
- Bogachev, V. I. , Pilipenko, A. Y. (2015). Strong solutions to stochastic equations with Lévy noise and a discontinuous drift coefficient. Dokl. Math . 92(1):471–475. DOI: 10.1134/S1064562415040213.
- Catellier, R. , Gubinelli, M. (2016). Averaging along irregular curves and regularisation of odes. Stochastic Processes Appl. 126(8):2323–2366. DOI: 10.1016/j.spa.2016.02.002.
- Fedrizzi, E. , Flandoli, F. (2013). Hölder flow and differentiability for SDEs with nonregular drift. Stochastic Anal. Appl . 31(4):708–736. DOI: 10.1080/07362994.2012.628908.
- Mohammed, S. E. A. , Nilssen, T. , Proske, F. (2015). Sobolev differentiable stochastic flows for SDE’s with singular coefficients: Applications to the transport equation. Ann. Probab . 43(3):1535–1576. DOI: 10.1214/14-AOP909.
- Flandoli, F. , Gubinelli, M. , Priola, E. (2010). Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift. Bull. Sci. Math . 134(4):405–422. DOI: 10.1016/j.bulsci.2010.02.003.
- Meyer-Brandis, T. , Proske, F. (2010). Construction of strong solutions of SDE’s via Malliavin calculus. J. Funct. Anal . 258(11):3922–3953. DOI: 10.1016/j.jfa.2009.11.010.
- Itô, K. , Nisio, M. (1964). On stationary solutions of a stochastic differential equation. J. Math. Kyoto Univ . 4(1):1–75. DOI: 10.1215/kjm/1250524705.
- Flandoli, F. , Gess, B. , Scheutzow, M. (2017). Synchronization by noise for order-preserving random dynamical systems. Ann. Probab . 45(2):1325–1350. DOI: 10.1214/16-AOP1088.
- Aryasova, O. , Pilipenko, A. (2019). On exponential decay of a distance between solutions of an SDE with non-regular drift. Theory Stochast Process . 24(40):1–13.
- Scheutzow, M. , Schulze, S. (2017). Strong completeness and semi-flows for stochastic differential equations with monotone drift. J. Math. Anal. Appl. 446(2):1555–1570. DOI: 10.1016/j.jmaa.2016.09.049.
- Scheutzow, M. (2013). A stochastic Gronwall lemma. Infin. Dimens. Anal. Quantum. Probab. Relat. Top. 16(02):1350019. DOI: 10.1142/S0219025713500197.