Convergence of stochastic processes with jumps to di!usion processes is investigated in the case when the limit process has discontinuous coe$cients. An example is given in which the diffusion approximation of a queueing model yields a di!usion process with discontinuous di!usion and drift coe$cients. c © 2002 Elsevier Science B.V. All rights reserved. MSC: 60B10; 60K25

This paper begins by describing the Polya urn process. Next, distributions of ball counts and ball proportions are derived. These derivations should provide the reader with an understanding of how urn processes behave. After this intuition is developed, a stochastic approximation of the process is derived. This way, the relationship between the stochastic results and the previously derived resu...

In Dekel and Feinberg (2004) we suggested a test for discovering whether a potential expert is informed of the distribution of a stochastic process. This category test requires predicting a “small”– category I – set of outcomes. In this paper we show that under the continuum hypothesis there is a category test that cannot be manipulated, i.e. such that no matter how the potential expert randomi...

We establish weak convergence of partial sums of tempered fractional time series (TFTS) to a stochastic process which we call a tempered Gaussian Hermite process (TGHP). We also introduce the Wiener integral with respect to TGHP, and establish weak convergence of weighted sums of TFTS to this Wiener integral.

Let ( fn)n 1 be a stochastic process adapted to the filtration (~’n)n o. Denoting by. (gn)Nn=1 the predictable projection of this process, i.e., gn = we show that the inequality [E( | gn |q)p/q]1/p 2 [E( I fn Iq)pI9 ] lip or, in more abstract terms ~(gn)Nn=1~Lp(lqN) ~ 2~(fn)Nn=1~Lp(lyN) holds true (with the obvious interpretation in the case of p = oo or g = oo). Several similar results, pertai...

The model introduced in this article is designed to provide a consistent representation for both the real-world and pricing measures for the credit process. We find that good agreement with historical and market data can be achieved across all credit ratings simultaneously. The model is characterized by an underlying stochastic process that represents credit quality and default events are assoc...

X(n) = X1(n1) + · · ·+XN (nN ), n ∈ N0 . Here, nj denotes the jth coordinate of n ∈ N0 . We are following the standard convention of starting (ordinary) random walks at the origin. That is, Xj(0) = 0 for all j = 1, . . . , N . From now on, N will always denote the temporal dimension and d the spatial one, to use the standard language of stochastic processes. In order to describe a natural parti...

This series of lectures is devoted to the study of the statistical properties of dynamical systems. When equipped with an invariant measure, a dynamical system can be viewed as a stochastic process. Many questions and results can be borrowed from probability theory and lead to many important results. On the other hand, the context of differential geometry often present in the phase space leads ...

This paper presents a method of fault prognostics and reliability estimation for DC motor using time series modeling procedure based on DC motor performance degradation data. DC motor performance degradation data are treated as a time series data and stochastic process are utilized to describe the degradation process for predicting long-term trend. A degradation test is processed for DC motor u...

Many of the lecturers here expressed their opinion that the primary task of statistics departments is to produce truly professional statisticians. However at least a part of the statisticians must have a serious mathematical background especially in probability theory, stochastic processes and mathematical statistics. The new term stochastics is very suitable for these three disciplines. Scient...