Francisco J. Piera

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In this paper we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R n + that satisfies certain finiteness conditions, we characterize the Fokker-Planck equation. We then provide necessary and sufficient conditions for the existence of(More)
We consider reflected jump-diffusions in the orthant n + with time-and state-dependent drift, diffusion and jump-amplitude coefficients. Directions of reflection upon hitting boundary faces are also allow to depend on time and state. Pathwise comparison results for this class of processes are provided, as well as absolute continuity properties for their(More)
In this paper we study the boundary characteristics of reflected diffusions with jumps in the positive orthant. We consider a model with oblique reflections and study the reflection map in terms of the local time at the boundary (or reflection) faces of R n +. In particular, we show that these last processes coincide (up to a multiplicative constant) and(More)
We prove some new pathwise comparison results for single class stochas-tic fluid networks. Under fairly general conditions, monotonicity with respect to the (state-and time-dependent) routing matrices is shown. Under more restrictive assumptions , monotonicity with respect to the service rates is shown as well. We conclude by using the comparison results to(More)
We consider a general stochastic input-output dynamical system with output evolving in time as the solution to a functional coefficients, Itô's stochastic differential equation, excited by an input process. This general class of stochastic systems encompasses not only the classical communication channel models, but also a wide variety of engineering systems(More)
— We consider a stochastic dynamical system whose output evolves in time as the solution to a functional coefficients, Itô's stochastic differential equation, excited by an input process. This general class of stochastic systems encompasses a wide variety of engineering models appearing through a whole range of applications, extending in particular the(More)
We consider a general stochastic input-output dynamical system with output evolving in time as the solution to a functional coefficients, Itô's stochastic differential equation, excited by an input process. This general class of stochastic systems encompasses not only the classical communication channel models, but also a wide variety of engineering systems(More)
Outline Motivation Some background-SRBM Jump Diffusions with constant reflections Jump diffusions with state dependent reflections Necessary and sufficient conditions for "product-form" Stability and convergence Conclusions ECE, University of Waterloo – p.2/50 Motivation Identifying stationary distributions of reflected diffusions with jumps-queues with(More)