This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. Finally, the error analysis and some numerical examples are provided...

In this paper, we consider a class of impulsive stochastic Volterra-Levin equations. By establishing a new integral inequality, some sufficient conditions for the existence and global attractivity of periodic solution for impulsive stochastic Volterra-Levin equations are given. Our results imply that under the appropriate linear periodic impulsive perturbations, the impulsive stochastic Volterr...

in this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional brownian motion in a hilbert space. we establish the existence and uniqueness of mild solutions for these equations under non-lipschitz conditions with lipschitz conditions being considered as a special case. an example is provided to illustrate the theory

the stochastic models for ship heave motion in irregular sea waves based on white and colored noises are examined. for this purpose the deterministic model transfers to stochastic models by adding different noise terms in force and then these models are solved analytically and numerically. finally an investigation is undertaken to examine the parameter estimation problem of second order stochas...

In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we study a state observation problem for stochastic hyperbolic equations. As a consequence, we also establish a unique cont...

The BMOmartingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) inRp (p ∈ [1,∞)) and backward stochastic differential equations (BSDEs) in Rp × Hp (p ∈ (1,∞)) and in R∞ × H∞, with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman’s inequality plays a crucial role in the development of our theory, wh...

In view of the extensive use of stochastic integrals and stochastic differential equations in modeling of systems in engineering, and economic systems especially in mathematical finance and other applied problems, it is necessary to find whether there are good approximants to the stochastic integrals and the stochastic differential equations which can be used for simulation purposes. Some work ...

As a Generalization to [37] where the dimension-free Harnack inequality was established for stochastic porous media equations, this paper presents analogous results for a large class of stochastic evolution equations with general monotone drifts. Some ergodicity, compactness and contractivity properties are established for the associated transition semigroups. Moreover, the exponential converge...