We consider a Lévy process with no negative jumps, reflected at a stochastic boundary that is a positive constant multiple of an age process associated with a Poisson process. We show that the stability condition for this process is identical to the one for the case of reflection at the origin. In particular, there exists a unique stationary distribution that is independent of initial condition...

Assume that a stochastic process can be approximated, when some scale parameter gets large, by a fluid limit (also called “mean field limit”, or “hydrodynamic limit”). A common practice, often called the “fixed point approximation” consists in approximating the stationary behaviour of the stochastic process by the stationary points of the fluid limit. It is known that this may be incorrect in g...

Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X and that f(X) is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times λn along which we will be able to estimate the conditional expectation E(f(Xλn+1)|X0, . . . , Xλn) from the observ...

In [5] we define a stationary tangent process, or a locally optimal stationary approximation, to a real non-stationary smooth Gaussian process. This paper extends the idea by constructing a discrete tangent – a “locally” optimal stationary approximation – for a discrete time, real Gaussian process. Analogously to the smooth case, our construction relies on a generalization of the recursion form...

The economic crisis in Argentina around year 2002 provides a unique opportunity for Econophysics studies. The available data on individual income are analyzed to show that they correspond to non stationary states. However, the rather restricted size of the data survey imposes difficulties that must be overcome through a careful analysis, for a reliable use. A new method of data treatment is pre...

In this paper we study a storage process or a liquid queue in which the input process is the local time of a positively recurrent stationary diffusion in stationary state and the potential output takes place with a constant deterministic rate. For this storage process we find its stationary distribution and compute the joint distribution of the starting and ending times of the busy and idle per...

In this paper, we consider the stationary density function of the doubly skew Ornstein-Uhlenbeck process. We present the explicit formula for the stationary density function and show that this process is positive Harris recurrent and geometrically ergodic. We expand our method to the more general cases in which the multiple parameters are present and we try to consider the stability of the skew...

For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form non-stationary solutions. The methods used include the classical Laplace cascade method as well as its recent generalizations for systems with more than 2 eq...

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a). This family contains various popular GARCH models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.

The late-time behaviour of the Einstein-dust system is well understood for homogeneous spacetimes. For the case of Bianchi I we have been able to show that the late-time behaviour of the Einstein-Vlasov system is well approximated by the Einstein-dust system assuming that one is close to the unique stationary solution which is the attractor of the Einstein-dust system.