arXiv subjects

Huizhong Appleby-Wu

Publications and source records attributed to Huizhong Appleby-Wu.

3 recordsLinked to original sources

arXiv2013

On the almost sure running maxima of solutions of affine neutral stochastic functional differential equations

This paper studies the large fluctuations of solutions of finite--dimensional affine stochastic neutral functional differential equations with finite memory, as well as related nonlinear equations. We find conditions under which the exact almost sure growth rate of the running maximum of each component of the system can be determined, both for affine and nonlinear equations. The proofs exploit the fact that an exponentially decaying fundamental solution of the underlying deterministic equation is sufficient to ensure that the solution of the affine equation converges to a stationary Gaussian process.

math.PR↗

arXiv2013

On the Existence and Uniqueness of Solutions of Stochastic Equations of Neutral Type

This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness of solutions of NSFDEs for many important classes of functional, and parallel the conditions used to ensure existence and uniqueness of solutions of related deterministic neutral equations. Exponential estimates on the almost sure and p--th mean rate of growth of solutions under the weaker existence conditions are also given.

math.PR↗

arXiv2013

Recurrent Solutions of Stochastic Differential Equations with Non-constant Diffusion Coefficients which obey the Law of the Iterated Logarithm

By using a change of scale and space, we study a class of stochastic differential equations (SDEs) whose solutions are drift--perturbed and exhibit behaviour analogous to standard Brownian motion including to the Law of the Iterated Logarithm (LIL). Sufficient conditions ensuring that these processes obey the LIL are given.

math.PR↗