Consider the following Markov chain, for ; ; p; q 2 (0; 1). Find all the recurrent and transient classes. Given that we start in state 2, what is the probability that we will reach state 0 before ...

Journal of Applied Probability and Advances in Applied Probability have for four decades provided a forum for original research and reviews in applied probability, mapping the development of ...

Let (Xn)n1=1, be a sequence of i.i.d. random variables distributed uniformly in [ 1; 1]. Show that the following sequences (Yn)n1=1 converge in probability to some limit. n (a) Yn = Qi=1 Xi. (b) Yn = ...

CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process.

Departamento de Matemáticas, Facultad de Ciencias, Mexico City, Mexico. Department of Mathematics, California State University Channel Islands, Camarillo, USA. There is a wide literature on Large ...