Abstract The stochastic fluid-fluid model (SFFM) is a Markov process $$\{(X_t,Y_t,\varphi _t),t\ge 0\}$$ { ( X t , Y φ ) ≥ 0</mml:mn...

Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study stochastic relations, which may be viewed as natural generalizations of stochastic orders. This generalization is motivated by the observation that for the stoc...

In his seminal paper from 1978, Ross set up a few conjectures which formalize a common belief that more variable arrival processes lead to worse performance in queueing systems. We study these types of problems for Cox/GI/1/∞, Cox/GI/∞/∞, and Cox/GI/1/0 systems. Assumptions are stated in terms of ≤idcx-regularity. For example, in the class of stationary Markov processes, the regularity property...

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized white noise process, which may be Gaussian or not (e.g., Laplace, impulsive Poisson or alpha stable). This allows for a conceptual decouplin...

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized white noise process, which may be Gaussian or not (e.g., Laplace, impulsive Poisson, or alpha stable). This allows for a conceptual decoupli...

Definition 1 (Time Series). A time series is a sequence of observations ordered with respect to a time index t, taking values in an index set S. If the set S contains a finite or countable number of elements we speak of discrete-time time series and the generic observation is indicated with the symbol yt, while if S is a continuum we have a continuous-time time series, whose generic observation...

By construction, the time series for radiative forcing that are used to run the 20c3m experiments, which are implemented by climate models, impart non-stationary movements (either stochastic or deterministic) to the simulated time series for global surface temperature. Here, we determine whether stochastic or deterministic trends are present in the simulated time series for global surface tempe...