# Probability and random processes

@inproceedings{Grimmett1982ProbabilityAR, title={Probability and random processes}, author={Geoffrey R. Grimmett and David R. Stirzaker}, year={1982} }

Events and their probabilities random variables and their distributions discrete random variables continuous random variables generating functions and their applications Markov chains convergence of random variables random processes stationary processes renewals queues Martingales diffusion processes. Appendices: Foundations and notations history and varieties of probability John Arburthnot's preface to "Of the Laws of Chance" (1692).

## 2,687 Citations

Concepts in Probability and Stochastic Modeling

- Mathematics
- 1994

1. Basic Probability 2. Discrete Random Variables 3. Special Discrete Random Variables 4. Markov Chains 5. Continuous Random Variables 6. Special Continuous Random Variables 7. Markov Counting and…

Renewal Theory and Its Applications

- Mathematics
- 2014

We have seen that a Poisson process is a counting process for which the times between successive events are independent and identically distributed exponential random variables. One possible…

Stochastic processes in science, engineering, and finance

- Mathematics
- 2006

Probability Theory Basics of Stochastic Processes Random Point Processes Markov Chains in Discrete Time Markov Chains in Continuous Time Martingales Brownian Motion

Directed random walks in random environments

- Mathematics
- 1991

We use holding time methods to study the asymptotic behavior of pure birth processes with random transition rates. Both the normal and slow approaches to infinity are studied. Fluctuations are shown…

Finite Markov Chains and Algorithmic Applications

- Mathematics
- 2002

1. Basics of probability theory 2. Markov chains 3. Computer simulation of Markov chains 4. Irreducible and aperiodic Markov chains 5. Stationary distributions 6. Reversible Markov chains 7. Markov…

Functional Analysis for Probability and Stochastic Processes: An Introduction

- Mathematics
- 2005

Preface 1. Preliminaries, notations and conventions 2. Basic notions in functional analysis 3. Conditional expectation 4. Brownian motion and Hilbert spaces 5. Dual spaces and convergence of…

Approximation for the Normal Inverse Gaussian Process Using Random Sums

- Mathematics
- 2009

Abstract We approximate the normal inverse Gaussian (NIG) process with random summations. The random sum we introduce is a random walk subordinated to the first passage time of another independent…

Probability on Graphs: Random Processes on Graphs and Lattices

- Mathematics
- 2018

Preface 1. Random walks on graphs 2. Uniform spanning tree 3. Percolation and self-avoiding walk 4. Association and influence 5. Further percolation 6. Contact process 7. Gibbs states 8.…

Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning

- Mathematics
- 2003

1. Measure theory and probability 2. Independence and conditioning 3. Gaussian variables 4. Distributional computations 5. Convergence of random variables 6. Random processes.

A class of infinitely divisible distributions connected to branching processes and random walks

- Mathematics
- 2002

A class of infinitely divisible distributions on {0,1,2,…} is defined by requiring the (discrete) Levy function to be equal to the probability function except for a very simple factor. These…

## References

The analysis of time series (5th edn

- Birkhauser,
- 1960