Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods

نویسندگان

چکیده

Abstract The equivalence of p th ( > 0 ) moment stability between stochastic differential delay equations and their numerical methods is studied under the assumptions that are strongly convergent have bounded in finite time.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Stochastic Volterra integro-differential equations: stability and numerical methods

We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation ẋ(t) = αx(t) + β ∫ t 0 x(s)ds+ σx(t− τ )Ẇ (t), where α, β, σ, τ ≥ 0 are real constants, and W (t) is a standard Wiener process. We adopt the shorthand notation of ẋ(t) to represent the differential dx(t) etc. Our choice of test equation is a stoc...

متن کامل

Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

متن کامل

pth Moment Noise-to-State Stability of Stochastic Differential Equations with Persistent Noise

This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential equation and does not decay with time. The class of systems we consider exhibit disturbance attenuation outside a closed, not necessarily bounded, set. We identify...

متن کامل

Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler–Maruyama (EM) method fails to...

متن کامل

Numerical Methods for Stochastic Differential Equations

Approximately a quarter century ago, very early in my career when I was publishing rather theoretical results about stochastic differential equations, I received a letter (this predates e-mail) from a fellow researcher who had seen my work and was asking if I had an algorithm suitable for implementing my ideas on a computing machine. Not only did I not have such an algorithm, the idea had not o...

متن کامل

ذخیره 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: Statistics & Probability Letters

سال: 2021

ISSN: ['1879-2103', '0167-7152']

DOI: https://doi.org/10.1016/j.spl.2020.108952