Nonlocal Stochastic Differential Equations Research Articles

Nonlocal stochastic differential equations with time‐varying delay driven by G‐Brownian motion

This article studies a class of nonlocal stochastic differential equations driven by G‐Brownian motion (G‐NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G‐Lyapunov functional and ψ‐type function.

Existence of Solutions and Approximate Controllability of Fractional Nonlocal Stochastic Differential Equations of Order $$1<q\le 2$$ 1 < q ≤ 2 with Infinite Delay and Poisson Jumps

In this paper, we investigate the existence of mild solutions and the approximate controllability of a class of nonlinear fractional stochastic differential equations of order \(1<q\le 2\) with infinite delay and Poisson jumps which satisfies the nonlocal conditions in Hilbert space. The existence of mild solutions is proved by using Sadovskii’s fixed point theorem. Also the approximate controllability of the nonlinear fractional nonlocal stochastic differential equations of order \(1<q\le 2\) with infinite delay and Poisson jumps is checked by using Lebesgue dominated convergence theorem. Finally an example is included to illustrate the results.

A class of stochastic differential equations with expectations in the coefficients

This paper considers a class of nonlocal stochastic differential equations with time-varying delay whose coefficients are dependent on expectations. By applying the M-matrix technique, the existence and uniqueness of the global solution of nonlocal stochastic differential delay equations is studied. A class of moment estimates of solutions is also considered. The results improve our previous work (Hu and Huang (2012) [1]). An example is provided to illustrate the effectiveness of our results.

Existence results and the moment estimate for nonlocal stochastic differential equations with time-varying delay

This paper considers a class of nonlocal stochastic differential equations with time-varying delay whose coefficients are dependent on the p th moment. By applying the fixed point theorem, the existence and uniqueness of the solution of nonlocal stochastic differential delay equations is studied. Also, a class of moment estimates of solutions is considered. The results are a generalization and continuation of the recent results on this issue. An example is provided to illustrate the effectiveness of our results.

Nonlocal stochastic differential equations: Existence and uniqueness of solutions

The focus of interest is the existence of strong solutions to stochastic functional differential equations which are not restricted to pathwise dependencies. Indeed, the evolution of the wanted random process may be prescribed by its current features being nonlocal with respect to the probability space — like the expected value and second moments. This result is concluded from Cauchy-Lipschitz Theorem for mutational equations (a form of generalized ODEs beyond vector spaces) and a new aspect of weakening their a priori requirements.