Itô Differential Representation of Singular Stochastic Volterra Integral Equations

A numerical method for solving m-dimensional stochastic Itô-Volterra integral equations by stochastic operational matrix

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 (...

Haar Wavelets Approach For Solving Multidimensional Stochastic Itô - Volterra Integral Equations ∗

A new computational method based on Haar wavelets is proposed for solving multidimensional stochastic Itô-Volterra integral equations. The block pulse functions and their relations to Haar wavelets are employed to derive a general procedure for forming stochastic operational matrix of Haar wavelets. Then, Haar wavelets basis along with their stochastic operational matrix are used to approximate...

strong approximation for itô stochastic differential equations

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

Weakly Singular Volterra and Fredholm-volterra Integral Equations

Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...