Some analytic approximations for neutral stochastic functional differential equations

Some analytic approximations for backward stochastic differential equations

“…is the determining sequence of the Z-algorithm, analogously to the paper [10] and Zuber's paper [23].…”

“…This is the most important example. If in (29) we take that ξ n = ξ, λ n = λ n = λ in = 0, n ∈ N 0 , we obtain the Picard iterations (4). All conditions of Theorem 2.2 are satisfied, and it yields that the sequence of iteration (x n (t), y n (t)), t ∈ [0, T], n ∈ N 0 converges with probability one to the solution (x(t), y(t)), t ∈ [0, T] of Eq.…”

“…Janković [7,8] presented an analogous analytic method for the forward stochastic differential equation of the Itô type, while Janković and Jovanović [9] extended Zuber's approach to various classes of stochastic hereditary differential equations. Recently, Janković, Vasilova and Krstić [10] adapted Zalgorithm for neutral stochastic functional differential equations.…”

Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps

“…For example, conditions of the existence and stability of the analytical solution are given in [14][15][16][17][18][19][20]. Various efficient computational methods are obtained and their convergence and stability have been studied in [21][22][23][24][25].…”

Exponential Stability of Neutral Stochastic Functional Differential Equations with Two-Time-Scale Markovian Switching

“…In many practical dynamical systems such as neural networks, computer aided design, population ecology, chemical process simulation, and automatic control, stochastic differential equations represent the class of important dynamics (see [1][2][3][4]). During the recent several years, the asymptotic properties of neutral stochastic functional differential equations have been investigated by many authors (see [5][6][7][8][9][10][11][12][13][14]). Mao [10,11] gave the exponential stability of neutral stochastic functional differential equations by using the Razumikhintype theorems.…”