References
- Coddington, E. A., Levinson, N. (1955). Theory of Ordinary Differential Equations. New York: McGraw-Hill.
- Bell, D. R., Mohammed, S. (1989). On the solution of stochastic ordinary differential equations via small delays. Stoch. Int. J. Probab. Stoch. Process. 28:293–299. DOI: 10.1080/17442508908833598.
- Mao, X. (1991). Approximate solutions for a class of stochastic evolution equations with variable delays. Numer. Funct. Anal. Optim. 12(5–6):525–533. DOI: 10.1080/01630569108816448.
- Mao, X. (1994). Approximate solutions for a class of stochastic evolution equations with variable delays II. Numer. Funct. Anal. Optim. 15(1–2):65–76. DOI: 10.1080/01630569408816550.
- Turo, J. (1996). Carathéodory approximation solutions to a class of stochastic functional differential equations. Appl. Anal. 61(1–2):121–128. DOI: 10.1080/00036819608840450.
- Liu, K. (1998). Carathéodory approximate solutions for a class of semilinear stochastic evolution equations with time delays. J. Math. Anal. Appl. 220(1):349–364. DOI: 10.1006/jmaa.1997.5889.
- Mao, W., Hu, L., Mao, X. (2018). Approximate Solutions for a Class of Doubly Perturbed Stochastic Differential Equations. Advances in Difference Equations. DOI: 10.1186/s13662-018-1490-5.
- Revuz, D., Yor, M. (2005). Continuous Martingales and Brownian Motion. Berlin: Springer.
- Chaumont, L., Doney, R. A. (1999). Pathwise uniqueness for perturbed versions of brownian motion and reflected Brownian motion. Probab. Theory Related Fields. 113(4):519–534. DOI: 10.1007/s004400050216.
- Doney, R. A., Zhang, T. (2005). Perturbed skorohod equations and perturbed reflected diffusion processes. Ann. Inst. H. Poincare-Probab. Stat. 41(1):107–121. DOI: 10.1016/j.anihpb.2004.03.005.
- Étoré, P., Martinez, M. (2018). Time inhomogeneous stochastic differential equations involving the local time of the unknown process, and associated parabolic operators, stochastic. Process. Appl. 128(8):2642–2687. DOI: 10.1016/j.spa.2017.09.018.
- Le Gall, J.-F. (1984). One-dimensional stochastic differential equations involving the local times of the unknown process, In: Stochastic Analysis and Applications (Swansea 1983), Lecture Notes in Math. Berlin: Springer, p.51–82.
- Ouknine, Y. (1993). Quelques identites sur les temps locaux et unicite des solutions dequations differentielles stochastiques avec reflection. Stoch. Process. Appl. 48(2):335–340. DOI: 10.1016/0304-4149(93)90052-6.
- Semrau, A. (2007). Euler’s approximations of weak solutions of reflecting SDEs with discontinuous coefficients. Bull. Polish Acad. Sci. Math. 55(2):171–182. DOI: 10.4064/ba55-2-8.
- Belfadli, R., Hamadène, S., Ouknine, Y. (2009). On one-dimensional stochastic differential equations involving the maximum process. Stoch. Dyn. 9(2):277–292. DOI: 10.1142/S0219493709002671.
- Bouhadou, S., Ouknine, Y. (2013). On the time inhomogeneous skew Brownian motion. Bull. Sci. Math. 137(7):835–850. DOI: 10.1016/j.bulsci.2013.02.001.
- Étoré, P., Martinez, M. (2012). On the existence of a time inhomogeneous skew brownian motion and some related laws. Electron. J. Probab. 17:1–27.
- Bihari, I. (1956). A generalization of a lemma of bellman and its application to uniqueness problem of differential equations. Acta Math. Acad. Sci. Hung. 7:71–94.