[PDF] Top 20 Stability of numerical method for semi linear stochastic pantograph differential equations

... differential equations played an important role in application areas, such as physics, biology, economics, and finance ...[–]. Stochastic pantograph differential equa- tions are particular cases of ... See full document

... (BEM) method strongly converges to the solution of the SDE with one-sided Lipschitz drift and linearly growing diffusion ...for numerical schemes only cover SDEs where the diffusion coefficients have at ... See full document

... Actually, many interesting works have been devoted to (A), i.e., given the SDE is stable under certain conditions, some numerical method can reproduce such a stability. We just mention some of the ... See full document

... of numerical methods for stochastic differential equations (SDEs) has recently attracted an increasing ...of stability, i.e., almost sure stability [–] and moment stability ... See full document

... exponential stability of stochastic differential equations (SDEs) is shared with that of a numerical ...the stochastic theta method is p th moment exponentially stable for a ... See full document

... the stability. Intuitively, even though a numerical method such as the Euler–Maruyama can match the stability properties of a single linear SDE for sufficiently small ∆ > 0, it is ... See full document

... the stochastic ver- sions of the LaSalle theorem, from which follows the almost sure asymptotic stability of SDEs and ...the stability of stochastic difference equations has been exam- ... See full document

... a numerical method, it is of practical importance to study the behavior of the global ...The numerical solution y n is expected to behave as the exact solution y ( x n ) does as x n approaches ...of ... See full document

... addressing numerical methods, because they play an important role to educe a realistic view of the solution behaviour of such ...the numerical analysis of SDDEs whose time lag is a dis- crete, see, ... See full document

... Neutral stochastic functional differential equations (NSFDEs) play a key role in model- ing physical, technical, biological and economic dynamic systems such as predicting op- tion pricing and the growth of ... See full document

... the stability analysis of the under- lying numerical scheme for the non-linear SDEs ...the numerical scheme is not stable, then the simulated path may diverge substantially from the exact ... See full document

... asymptotic stability and boundedness arising from automatic ...and linear growth condition. However, the linear growth condition is usually violated in many practical ...and stability of ... See full document

... exponential stability criteria by the methods of Lyapunov functions and M-matrices for a class hybrid neutral pantograph stochastic differential ...exponential stability criterion and ... See full document

... By Ito’s formula and the delay term of the equation, we give the proof of Theorem .. The highlight of the proof is that we give the mean square boundedness of the solution to the equation by dividing the interval into ... See full document

... Here η has finite q-variation, with q ∈ [ 1 , 2 ) and the last term is a priori not well-defined. There are several approaches to make sense of such a “rough” PDE (or pathwise SPDEs). We shall employ the solution concept ... See full document

... on stability and numerical solution of SDEs with jumps under nonlinear growth con- ...formula, stochastic inequality and nonnegative semi-martingales convergence theorem, we prove that SDEs ... See full document

... ordinary differential equations which contain random constant or random variables are well known topics which are called the random ordinary differential ...random differential ... See full document

... Mao, Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions, Applied Mathematics and Computation, 217(2011), ...and stability ... See full document

... Razumikhin-type stability theorems of neutral stochastic functional differential equations (NFDEs) were investigated by several authors, but there was almost no Razumikhin-type theorems on the general ... See full document

... the method we will use for our ...the numerical meth- ods for SDE. First, we represent a stochastic Taylor expansion and we obtain the Euler- Maruyama [11] and Milstein methods [12] from the ... See full document