On solutions of neutral stochastic delay Volterra equations with singular kernels

On solutions of neutral stochastic delay Volterra equations with singular kernels∗

In this paper, existence, uniqueness and continuity of the adapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition, continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.

Regularity of Solutions to Stochastic Volterra Equations with Infinite Delay

The paper gives necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a ddimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used.

Solutions for Singular Volterra Integral Equations

0 gi(t, s)[Pi(s, u1(s), u2(s), · · · , un(s)) + Qi(s, u1(s), u2(s), · · · , un(s))]ds, t ∈ [0, T ], 1 ≤ i ≤ n where T > 0 is fixed and the nonlinearities Pi(t, u1, u2, · · · , un) can be singular at t = 0 and uj = 0 where j ∈ {1, 2, · · · , n}. Criteria are offered for the existence of fixed-sign solutions (u∗1, u ∗ 2, · · · , u ∗ n) to the system of Volterra integral equations, i.e., θiu ∗ i (...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay

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