36-754, Advanced Probability II or Almost None of the Theory of Stochastic Processes

36-754, Advanced Probability II or Almost None of Stochastic Processes

FUZZY INFORMATION AND STOCHASTICS

In applications there occur different forms of uncertainty. The twomost important types are randomness (stochastic variability) and imprecision(fuzziness). In modelling, the dominating concept to describe uncertainty isusing stochastic models which are based on probability. However, fuzzinessis not stochastic in nature and therefore it is not considered in probabilisticmodels.Since many years t...

Almost None of the Theory of Stochastic Processes A Course on Random Processes, for Students of Measure-Theoretic Probability, with a View to Applications in Dynamics and Statistics

Second Moment of Queue Size with Stationary Arrival Processes and Arbitrary Queue Discipline

In this paper we consider a queuing system in which the service times of customers are independent and identically distributed random variables, the arrival process is stationary and has the property of orderliness, and the queue discipline is arbitrary. For this queuing system we obtain the steady state second moment of the queue size in terms of the stationary waiting time distribution of a s...

Confidence Interval Estimation of the Mean of Stationary Stochastic Processes: a Comparison of Batch Means and Weighted Batch Means Approach (TECHNICAL NOTE)

Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the cor...