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Chenggui Yuan

Publications and source records attributed to Chenggui Yuan.

At least 73 records · Page 4Linked to original sources
arXiv2016

Convergence Rate of Euler-Maruyama Scheme for SDEs with Rough Coefficients

In this paper, we are concerned with convergence rate of Euler-Maruyama scheme for stochastic differential equations with rough coefficients. The key contributions lie in (i), by means of regularity of non-degenerate Kolmogrov equation, we investigate convergence rate of Euler-Maruyama scheme for a class of stochastic differential equations, which allow the drifts to be Dini-continuous and unbounded; (ii) by the aid of regularization properties of degenerate Kolmogrov equation, we discuss convergence rate of Euler-Maruyama scheme for a range of degenerate stochastic differential equations, where the drift is locally Hölder-Dini continuous of order $\frac{2}{3}$ with respect to the first component, and is merely Dini-continuous concerning the second component.

math.PR↗
arXiv2016

Convergence of EM Scheme for Neutral Stochastic Differential Delay Equations

In this paper, we are concerned with convergence rate of Euler-Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) of neutral type, where the neutral term, the drift term and the diffusion term are allowed to be of polynomial growth. More precisely, for SDDEs of neutral type driven by Brownian motions, we reveal that the convergence rate of the corresponding EM scheme is one half; Whereas for SDDEs of neutral type driven by jump processes, we show that the best convergence rate of the associated EM scheme is close to one half.

math.PR↗
arXiv2016

Tamed EM scheme of Neutral Stochastic Differential Delay Equations

In this paper, we investigate the convergence of the tamed Euler-Maruyama (EM) scheme for a class of neutral stochastic differential delay equations. The strong convergence results of the tamed EM scheme are presented under global and local non-Lipschitz conditions, respectively. Moreover, under a global Lipschitz condition, we provide the rate of the convergence of tamed EM, which is smaller than the rate convergence of classical EM scheme one half.

math.PR↗
arXiv2016

Stochastic Delay Differential Equations with Jump Reflection: Invariant Measure

In this paper, we consider a class of multi-dimensional stochastic delay differential equations with jump reflection. Based on existence and uniqueness of the strong solution to the equation, we prove that the Markov semigroup generated by the segment process corresponding to the solution admits a unique invariant measure on the Skorohod space when the coefficients of equation satisfy a class of monotone conditions. Finally, we establish a relationship between the regulator and the local time of the solution and discuss a local time property at large time under the stationary setting.

math.PR↗
arXiv2015

Hypercontractivity for Functional Stochastic Partial Differential Equations

Explicit sufficient conditions on the hypercontractivity are presented for two classes of functional stochastic partial differential equations driven by, respectively, non-degenerate and degenerate Gaussian noises. Consequently, these conditions imply that the associated Markov semigroup is $L^2$-compact and exponentially convergent to the stationary distribution in entropy, variance and total variational norm. As the log-Sobolev inequality is invalid under the framework, we apply a criterion presented in the recent paper \cite{Wang14} using Harnack inequality, coupling property and Gaussian concentration property of the stationary distribution. To verify the concentration property, we prove a Fernique type inequality for infinite-dimensional Gaussian processes which might be interesting by itself.

math.PR↗
arXiv2015

A Strong Limit Theorem for Two-Time-Scale Fucntional Stochastic Differential Equations

This paper focuses on a class of two-time-scale functional stochastic differential equations, where the phase space of the segment processes is infinite-dimensional. It develops ergodicity of the fast component and obtains a strong limit theorem for the averaging principle in the spirit of Khasminskii's averaging approach for the slow component.

math.PR↗
arXiv2015

Hypercontractivity and Its Applications for Functional SDEs of Neutral Type

In this paper, we discuss hypercontractivity for the Markov semigroup $P_t$ which is generated by segment processes associated with a range of functional SDEs of neutral type. As applications, we also reveal that the semigroup $P_t$ converges exponentially to its unique invariant probability measure $μ$ in entropy, $L^2 (μ)$ and $\|\cdot\|_{\mbox{var}}$, respectively.

math.PR↗
arXiv2014

Almost Sure Asymptotic Stability for Regime-Switching Diffusions

In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the Perron-Frobenius theorem, and, with regard to the case of reversible Markov chain, via the principal eigenvalue approach; (ii) for regime-switching diffusions with countable state spaces by means of a finite partition trick and an M-Matrix theory. We then apply our theory to study the stabilization for linear switching models. Several examples are given to demonstrate our theory.

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

Approximation of Invariant Measures for Regime-Switching Diffusions

In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with a range of regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for regime-switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the "averaging condition" holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for regime-switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.

math.PR↗
arXiv2014

Hypercontractivity for Functional Stochastic Differential Equations

An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique invariant probability measure $μ$ in entropy, $L^2(μ)$ and the totally variational norm, and it is compact in $L^2(μ)$ for large $t>0$. This provides a natural class of non-symmetric Markov semigroups which are compact for large time but non-compact for small time. A semi-linear model which may not satisfy this sufficient condition is also investigated.

math.PR↗
arXiv2013

Stationary Distributions for Retarded Stochastic Differential Equations without Dissipativity

Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems in which both the drift and the diffusion coefficients depend only on the arguments with delays, the existing results become not applicable. This work uses a variation-of-constants formula to overcome the difficulties due to the lack of the information at the current time. This paper establishes existence and uniqueness of stationary distributions for retarded SDEs that need not satisfy dissipative conditions. The retarded SDEs considered in this paper also cover SDEs of neutral type and SDEs driven by Lévy processes that might not admit finite second moments.

math.PR↗
arXiv2013

Exponential Mixing for Retarded Stochastic Differential Equations

In this paper, we discuss exponential mixing property for Markovian semigroups generated by segment processes associated with several class of retarded Stochastic Differential Equations (SDEs) which cover SDEs with constant/variable/distributed time-lags. In particular, we investigate the exponential mixing property for (a) non-autonomous retarded SDEs by the Arzelà--Ascoli tightness characterization of the space $\C$ equipped with the uniform topology (b) neutral SDEs with continuous sample paths by a generalized Razumikhin-type argument and a stability-in-distribution approach and (c) jump-diffusion retarded SDEs by the Kurtz criterion of tightness for the space $\D$ endowed with the Skorohod topology.

math.PR↗
arXiv2013

Numerical Approximation of Stationary Distribution for SPDEs

In this paper, we show that the exponential integrator scheme both in spatial discretization and time discretization for a class of stochastic partial differential equations has a unique stationary distribution whenever the stepsize is sufficiently small, and reveal that the weak limit of the law for the exponential integrator scheme is in fact the counterpart for the stochastic partial differential equation considered.

math.PR↗
arXiv2012

Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds

By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.

math.PR↗
arXiv2012

Transportation Cost Inequalities for Neutral Functional Stochastic Equations

By using Girsanov transformation and martingale representation, Talagrand-type transportation cost inequalities, with respect to both the uniform and the $L^2$ distances on the global free path space, are established for the segment process associated to a class of neutral functional stochastic differential equations. Neutral functional stochastic partial differential equations are also investigated.

math.PR↗