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Perturbed nonlocal stochastic functional differential equations. (English) Zbl 07259349
The authors discuss the asymptotic behavior of the solution for a class of perturbed nonlocal stochastic functional differential equations. They evaluate the distance between the latter and of the unperturbed solution, in finite time-intervals, and on maximal intervals as the small perturbations tend to zero. These results non-trivially extend previous criteria, including some of the reviewer’s.
MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
34K50 Stochastic functional-differential equations
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[1] Hu, Y.; Wu, F., A class of stochastic differential equations with expectations in the coefficients, Nonlinear Anal., 81, 190-199 (2013) · Zbl 1261.34064
[2] Janković, S.; Jovanović, M., Perturbed stochastic hereditary differential equations with integral contractors, Comput. Math. Appl., 42, 871-881 (2001) · Zbl 0994.34044
[3] Janković, S.; Jovanović, M., Generalized stochastic perturbation-depending differential equations, Stoch. Anal. Appl., 20, 1281-1307 (2002) · Zbl 1016.60062
[4] Janković, S.; Jovanović, M., On perturbed nonlinear Itô type stochastic integrodifferential equations, J. Math. Anal. Appl., 269, 301-316 (2002) · Zbl 0996.60076
[5] Janković, S.; Jovanović, M., Functionally perturbed stochastic differential equations, Math. Nachr., 279, 1808-1822 (2006) · Zbl 1107.60033
[6] Janković, S.; Jovanović, M., Neutral stochastic functional differential equations with additive perturbations, Appl. Math. Comput., 213, 370-379 (2009) · Zbl 1221.34221
[7] Mao, X., Stochastic Differential Equations and Applications (1997), Chichestic, UK: Horwood, Chichestic, UK · Zbl 0874.60050
[8] Peter, K.; Thomas, L., A Peano-like theorem for stochastic differential equations with nonlocal sample dependence, Stoch. Anal. Appl., 31, 19-30 (2013) · Zbl 1273.60081
[9] Ren, Y.; Lu, S.; Xia, N., Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math., 220, 364-372 (2008) · Zbl 1152.34388
[10] Ren, Y.; Xia, N., Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput., 210, 72-79 (2009) · Zbl 1167.34389
[11] Ren, Y.; Chen, L., A note on the neutral stochastic functional differential equations with infinite delay and Poisson jumps in an abstract space, J. Math. Phys., 50, 082704 (2009) · Zbl 1223.34110
[12] Sheinkman, J.; LeBaron, B., Nonlinear dynamics and stock returns, J. Busines, 62, 311-337 (1989)
[13] Stoica, G., A stochastic delay financial model, Proc. Am. Math. Soc., 133, 1837-1841 (2005) · Zbl 1134.91464
[14] Thomas, L., Nonlocal stochastic differential equations: existence and uniqueness of solutions, Bol. Soc. Esp. Mat. Apl. SeMA, 51, 99-107 (2010) · Zbl 1242.60054
[15] Wu, F.; Hu, S., On a class of nonlocal stochastic functional differential equations with infinite delay, Stoch. Anal. Appl., 29, 713-721 (2011) · Zbl 1229.60076
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