Searcharxiv⌕ Search

arXiv subjects

Guangqiang Lan

Publications and source records attributed to Guangqiang Lan.

14 recordsLinked to original sources
arXiv2026

Stabilization of highly nonlinear hybrid stochastic differential delay equations by periodically intermittent feedback controls based on discrete-time observations with asynchronous switching

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous switching is designed. The upper bound of observation period as well as the lower bound of the control width are all obtained. Firstly, the finiteness and boundedness of the $p$-th moment of the solution are established under a generalized Khasminskii-type condition. Then reasonable conditions of control function, drift and diffusion coefficients are presented. Then exponential stability as well as the convergence rate of controlled system are proved. Finally, an example is presented to interpret the conclusion, which also indicates that the proportion of control interval has positive relation to the convergence rate.

math.OC↗
arXiv2023

Mean square exponential stability of numerical methods for stochastic differential delay equations

Mean square exponential stability of $θ$-EM and modified truncated Euler-Maruyama (MTEM) methods for stochastic differential delay equations (SDDEs) are investigated in this paper. We present new criterion of mean square exponential stability of the $θ$-EM and MTEM methods for SDDEs, which are different from most existing results under Khasminskii-type conditions. Two examples are provided to support our conclusions.

math.NA↗
arXiv2022

Convergence and exponential stability of modified truncated Milstein method for stochastic differential equations

In this paper, we develop a new explicit scheme called modified truncated Milstein method which is motivated by truncated Milstein method proposed by Guo (2018) and modified truncated Euler-Maruyama method introduced by Lan (2018). We obtain the strong convergence of the scheme under local boundedness and Khasminskii-type conditions, which are relatively weaker than the existing results, and we prove that the convergence rate could be arbitrarily close to 1 under given conditions. Moreover, exponential stability of the scheme is also considered while it is impossible for truncated Milstein method introduced in Guo(2018). Three numerical experiments are offered to support our conclusions.

math.NA↗
arXiv2018

Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations

The aim of this paper is to investigate strong convergence of modified truncated Euler-Maruyama method for neutral stochastic differential delay equations introduced in Lan (2018). Strong convergence rates of the given numerical scheme to the exact solutions at fixed time $T$ are obtained under local Lipschitz and Khasminskii-type conditions. Moreover, convergence rates over a time interval $[0,T]$ are also obtained under additional polynomial growth condition on $g$ without the weak monotonicity condition (which is usually the standard assumption to obtain the convergence rate). Two examples are presented to interpret our conclusions.

math.PR↗
arXiv2018

Polynomial stability of exact solution and a numerical method for stochastic differential equations with time-dependent delay

Polynomial stability of exact solution and modified truncated Euler-Maruyama method for stochastic differential equations with time-dependent delay are investigated in this paper. By using the well known discrete semimartingale convergence theorem, sufficient conditions are obtained for both bounded and unbounded delay $δ$ to ensure the polynomial stability of the corresponding numerical approximation. Examples are presented to illustrate the conclusion.

math.PR↗
arXiv2017

Strong convergence rates of modified truncated EM method for stochastic differential equations

Motivated by truncated EM method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler-Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact solutions to stochastic differential equations are investigated under given conditions in this paper. Compared with truncated EM method, the given numerical simulation strongly converges to the exact solution at fixed time $T$ and over a time interval $[0,T]$ under weaker sufficient conditions. Meanwhile, the convergence rates are also obtained for both cases. Two examples are provided to support our conclusions.

math.PR↗
arXiv2014

Exponential stability of the exact solutions and $θ$-EM approximations to neutral SDDEs with Markov switching

Exponential stability of the exact solutions as well as $θ$-EM ($\frac{1}{2}<θ\le 1$) approximations to neutral stochastic differential delay equations with Markov switching will be investigated in this paper. Sufficient conditions are obtained to ensure the $p$-th moment ($p\ge1$) and almost sure exponential stability of the exact solutions as well as $θ$-EM approximations ($p=2$). An example will be presented to support our conclusions.

math.PR↗
arXiv2014

The explicit solution and precise distribution of CKLS model under Girsanov transform

We study the relation between CKLS model and CIR model. We prove that under a suitable transformation, any CKLS model of order $\frac{1}{2}<γ<1$ or $γ> 1$ corresponds to a CIR model under a new probability space. Moreover, we get the explicit solution and the precise distribution of the CKLS model at any time $t$ under the new probability measure. We also give the moment estimation of CKLS model.

math.PR↗
arXiv2014

Polynomial and exponential stability of $θ$-EM approximations to a class of stochastic differential equations

Both the mean square polynomial stability and exponential stability of $θ$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\leθ\le 1$ by using an auxiliary function $F$ (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions.

math.NA↗
arXiv2014

Stochastic continuity, irreducibility and non confluence for SDEs with jumps

In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than those relevant conditions existing in the literature. We also provide an example to support our new conditions.

math.PR↗
arXiv2014

Existence and uniqueness of global strong solutions for SDEs with jumps under a new sufficient condition

In this paper, we investigate new sufficient conditions to ensure the existence of a unique global strong solution of stochastic differential equations with jumps. By using Euler approximation and by utilising a new test function $φ_δ$ (see the following definition (\ref{pntas1})), we prove that there is a unique global strong solution for the initial value problem of the equation. The condition we posed is even weaker than the local Lipschitzian continuity of the coefficients. We also present an example to show that our conditions are indeed weaker than those relevant conditions existing in the literature.

math.PR↗
arXiv2014

Large deviation principle of SDEs with non-Lipschitzian coefficients under localized conditions

Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is weaker than those relevant conditions existing in the literature. We consider at first the large deviation principle when $\int_0^t\sup_{x\in\mathbb{R}^d}||σ(s,x)||\vee|b(s,x)|ds=:C_t<\infty$ for any fixed $t$, then we generalize the conclusion to unbounded case by using bounded approximation program.

math.PR↗
arXiv2014

New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients

The object of the present paper is to find new sufficient conditions for the existence of unique strong solutions to a class of (time-inhomogeneous) stochastic differential equations with random, non-Lipschitzian coefficients. We give an example to show that our conditions are indeed weaker than those relevant conditions existing in the literature. We also derive moment estimations for the maximum process of the solution. Finally, we present a sufficient condition to ensure the non confluence property of the solution of time-homogeneous SDE which, in one dimension, is nothing but stochastic monotone property of the solution.

math.PR↗