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- W2556512977 abstract "Stability analysis of Ito equations with aftereffect attracts attention of many researchers (see e.g. [2, 3, 8, 10, 11]). On the other hand, stability of impulsive functional differential equations is popular in the literature as well (see e.g. [1,4]). In [7] we considered these two classes of equations together using the framework based on Azbelev’s W-method (see e.g. [2, 3, 5, 6]). Let (Ω,F , (Ft)t≥0,P) be a stochastic basis consisting of a probability space (Ω,F ,P) and an increasing, right-continuous family (a filtration) (Ft)t≥0 of complete σ-subalgebras of F . By E we denote the expectation on this probability space. The scalar stochastic processes Bi, i = 1, 2, . . . ,m form the standard m-dimensional Brownian motion on (Ft)t≥0 (see e.g. [9]). Below we use the following spaces: • L∞ consists of all scalar, essentially bounded functions on [0,∞) with the usual norm; • L q consists of all n-dimensional progressively measurable (with respect to the above stochastic basis) stochastic processes on [0,∞), whose trajectories are almost surely (a.s.) locally qintegrable if 1 ≤ q < ∞ and a.s. locally bounded if q = ∞; • kn contains all F0-measurable n-dimensional random variables, and we will put k1 = k in the sequel; • Dn contains all n-dimensional stochastic processes on [0,∞), which could be represented" @default.
- W2556512977 created "2016-11-30" @default.
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- W2556512977 date "2014-01-01" @default.
- W2556512977 modified "2023-09-27" @default.
- W2556512977 title "Stability of Linear Impulsive It^o Equations with Delay" @default.
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