Almost sure stability of the Euler–Maruyama method with random variable stepsize for stochastic differential equations
نویسندگان
چکیده
منابع مشابه
Almost Sure Exponential Stability of Stochastic Differential Delay Equations
This paper is concerned with the almost sure exponential stability of the multidimensional nonlinear stochastic differential delay equation (SDDE) with variable delays of the form dx(t) = f(x(t−δ1(t)), t)dt+g(x(t−δ2(t)), t)dB(t), where δ1, δ2 : R+ → [0, τ ] stand for variable delays. We show that if the corresponding (nondelay) stochastic differential equation (SDE) dy(t) = f(y(t), t)dt + g(y(t...
متن کاملA Variable Stepsize Implementation for Stochastic Differential Equations
Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge–Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this fo...
متن کاملAlmost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations
By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure exponential stability of the exact solution. Moreover, for sufficiently small stepsize, the decay rate as measured by the Lyapunov exponent can be re...
متن کاملAlmost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations
In this paper we shall discuss the almost sure exponential stability for a neutral differential difference equation with damped stochastic perturbations of the form d[x(t) −G(x(t − τ ))] = f(t, x(t), x(t − τ ))dt + σ(t)dw(t). Several interesting examples are also given for illustration. It should be pointed out that our results are even new in the case when σ(t) ≡ 0, i.e. for deterministic neut...
متن کاملAlmost sure and moment exponential stability of predictor-corrector methods for stochastic differential equations
This paper deals with almost sure and moment exponential stability of a class of predictorcorrector methods applied to the stochastic differential equations of Itô-type. Stability criteria for this type of methods are derived. The methods are shown to maintain almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions. A numerical experiment f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Algorithms
سال: 2016
ISSN: 1017-1398,1572-9265
DOI: 10.1007/s11075-016-0162-3