1st Edition
by Yaroslav Chabanyuk (Author), Anatolii Nikitin (Author), Uliana Khimka (Author)
The emergence of the theory of stochastic differential equations played a prominent role in the works of S.N. Bernshtain, M.M. Bogolyubov and M.M. Krylov. A systematic study of stochastic differential equations was first carried out by Y.I. Gichman. The concept of random evolution was introduced by Griego and Hersh (1969) and Bellman (1957).
Applications of such a model were derived from the work of Feng (1999), Fleming and Soner (2006), Feng and Kurtz (2006), which were stimulated by the problems of the stability of stochastic systems.
In the 1960s and 1970s, the problems associated with the theory of random evolution were actively investigated by American mathematicians R. Hersch, M. Pinskii, G. Papanikolau, T. Kurtts, R. Griego, L. Horossey (Skorokhod 1989; Sviridenko 1998; Skorokhod et al. 2002; Samoilenko et al. 2017) and others. In particular, G. Papanikolaou, D. Stroock and S. Varadan proposed a martingale approach for the proof of boundary theorems (Papanicolaou et al. 1977), Stroock using methods similar to solving the singular perturbation problem.
