Nonstandard construction of the stochastic integral and applications to stochastic differential equations. II

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

Stochastic Differential Equations and Applications

The expressions of solutions for general n × m matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential equations. As an application, some IR vector-valued inhomogeneous nonlinear stochastic differential equations are reduced to random differential equations, facilitating...

Application of DJ method to Ito stochastic differential equations

‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (2006) 753-763] to solve Ito stochastic differential equations‎. ‎The convergence of the method for Ito stochastic differential equations is assessed‎. ‎To verify efficiency of method‎, ‎some examples are ex...

Stochastic Differential Equations with Applications

Forward-Backward Doubly Stochastic Differential Equations with Random Jumps and Stochastic Partial Differential-Integral Equations

In this paper, we study forward-backward doubly stochastic differential equations driven by Brownian motions and Poisson process (FBDSDEP in short). Both the probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations (SPDIEs in short) and stochastic Hamiltonian systems arising in stochastic optimal control problems with random jum...