14 citations · 29 across the 15 of their papers we have counts for
17 papers
Wong--Zakai approximation of regime-switching SDEs via rough path theory
Jasper Barr, Giang T. Nguyen, Oscar Peralta
This paper investigates the convergence of Wong--Zakai approximations to regime-switching stochastic differential equations, generated by a collection of finite-variation approxima…
RAP-modulated Fluid Processes: First Passages and the Stationary Distribution
Nigel G. Bean, Giang T. Nguyen, Bo F. Nielsen +1
We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (R…
Wong--Zakai approximations with convergence rate for stochastic differential equations with regime switching
Giang T. Nguyen, Oscar Peralta
We construct Wong--Zakai approximations of time--inhomogeneous stochastic differential equations with regime switching (RSSDEs), and provide a convergence rate. %Given a family of…
An explicit solution to the Skorokhod embedding problem for double exponential increments
Giang T. Nguyen, Oscar Peralta
Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In…
Strong convergence to two-dimensional alternating Brownian motion processes
Guy Latouche, Giang T. Nguyen, Oscar Peralta
Flip-flop processes refer to a family of stochastic fluid processes which converge to either a standard Brownian motion (SBM) or to a Markov modulated Brownian motion (MMBM). In re…
Rate of Strong Convergence to Markov-modulated Brownian motion
Giang T. Nguyen, Oscar Peralta
In Latouche and Nguyen (2015), the authors constructed a sequence of stochastic fluid processes and showed that it converges weakly to a Markov-modulated Brownian motion (MMBM). He…
A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes
Nigel Bean, Giang T. Nguyen, Malgorzata M. O'Reilly +1
Introduced by Bean and O'Reilly (2014), a stochastic fluid-fluid process is a Markov processes , where the first fluid is driven by the Markov c…
Analysis of fluid flow models
Guy Latouche, Giang Nguyen
Markov-modulated fluids have a long history. They form a simple class of Markov additive processes, and were initially developed in the 1950s as models for dams and reservoirs, bef…
Doubling Algorithms for Stationary Distributions of Fluid Queues: A Probabilistic Interpretation
Nigel Bean, Giang T. Nguyen, Federico Poloni
Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returni…
Componentwise accurate Brownian motion computations using Cyclic Reduction
Giang T. Nguyen, Federico Poloni
Markov-modulated Brownian motion is a popular tool to model continuous-time phenomena in a stochastic context. The main quantity of interest is the invariant density, which satisfi…
Feedback control: two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundaries
Guy Latouche, Giang T. Nguyen
We consider a Markov-modulated Brownian motion with two boundaries at and , and allow for the controlling Markov chain to instantaneously und…
Slowing time: Markov-modulated Brownian motion with a sticky boundary
Guy Latouche, Giang T. Nguyen
We analyze the stationary distribution of regulated Markov modulated Brownian motions (MMBM) modified so that their evolution is slowed down when the process reaches level zero ---…
Componentwise accurate fluid queue computations using doubling algorithms
Giang T. Nguyen, Federico Poloni
Markov-modulated fluid queues are popular stochastic processes frequently used for modelling real-life applications. An important performance measure to evaluate in these applicati…
Two-dimensional fluid queues with temporary assistance
Guy Latouche, Giang T. Nguyen, Zbigniew Palmowski
We consider a two-dimensional stochastic fluid model with ON-OFF inputs and temporary assistance, which is an extension of the same model with in Mahabhashyam et al. (2…
Fluid approach to two-sided Markov-modulated Brownian motion
Guy Latouche, Giang T. Nguyen
We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has recently been…
The morphing of fluid queues into Markov-modulated Brownian motion
Guy Latouche, Giang T. Nguyen
Ramaswami showed recently that standard Brownian motion arises as the limit of a family of Markov-modulated linear fluid processes. We pursue this analysis with a fluid approximati…
Extinction probabilities of branching processes with countably infinitely many types
Sophie Hautphenne, Guy Latouche, Giang Nguyen
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabili…