A description in terms of phase and amplitude variables is given, for nonlinear oscillators subject to white Gaussian noise described by Itô stochastic differential equations. The stochastic differential equations derived for the amplitude and the phase are rigorous, and their validity is not limited to the weak noise limit. If the noise intensity is small, the equations can be efficiently solv...

In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with Lévy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to ...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...

Uncertain differential equations are a type of differential equations driven by canonical process, and are quite different from stochastic differential equations that are driven by Brownian motion. A solution of an uncertain differential equation is an uncertain process. This paper presents an analytic method to solve a particular class of nonlinear uncertain differential equations and gives so...

We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which ...

For a system governed by Itô-type nonlinear stochastic differential equation with state-dependent noise, the H2/H∞ control problem is considered, which combines the H2 optimization with the robust H∞ performance. A cross-coupled Hamilton-Jacobi equations associated with the nonlinear stochastic H2/H∞ control are obtained, based on which, sufficient conditions for designing the finite and infini...

This paper proposes a stochastic finite difference approach, based onhomogenous chaos expansion (SFDHC).The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using KarhunenLoève expansion, w...

Herein paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the circular symmetrical sandwich plates bending with isotropic face sheets and the nonlinear elastic core material. The method of constructing an analytical solution of nonlinear differential equations has been described. ...

in the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistatic approach (eqs) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.this...