This note establishes stationarity of a number of stochastic processes of interest in the study of Transport Protocols. For many of the processes studied in this note stationarity had been established before, but for one class the result is new. For that class, it was counterintuitive that stationarity was hard to prove. This note also explains why that class offered such stiff resistance. The ...

We comment on some points about the coding of stochastic processes by sequences of independent random variables. The most interesting question has to do with the standardness property of the filtration generated by the process, in the framework of Vershik’s theory of filtrations. Non-standardness indicates the presence of long memory in a purely probabilistic sense. We aim to provide a short, n...

Appendix A. There exists a Cox process with an a.s. C ∞ intensity coinciding with any finite dimensional prior. In this section we prove the proposition below. Proposition .1 Let Q be an (n + 1) dimensional continuous probability distribution whose density has support n+1 i=1 ]0, +∞[, and let x 1 ,. .. , x n be n points on a compact domain S ⊂ R d. There exists an almost surely non-negative and...

Stationary processes are stochastic processes whose probabilistic structure is unaffected by shifts in time. According to the interpretation of the term “probabilistic structure”, one distinguishes weak sense stationary processes, where only the covariance structure is supposed to be invariant, and strict sense stationary processes, for which all finitedimensional distributions have to remain t...

We are going to give necessary and suucient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes .

At any point in time, a cleared parcel of forest land (CPFL) used for swidden agriculture exists in either the fallow or in the non-fallow state. Further, the practice of swidden agriculture requires one to operate in an environment of uncertainty. These two points notwithstanding, there are virtually no probabilistic models of swidden agriculture that explicitly account for the above dichotomy...

Multivariate COGARCH(1,1) processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate Lévy process and the latent timevarying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices. After defining the COGARCH(1,1) process, we analyze its probabilistic propertie...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

this article aims at designing the mathematical model for aras dam reservoir in time operation with missions of agriculture needs safeguarding, water electric energy production and torrent controls. reservoir system relations determinate and these relations at framework of are determined and stochastic dynamic programming are calculated executive results of this model are presentation of guides...