Stochastic Processes
Random processes indexed by time: Markov chains, Lévy, and Gaussian processes.
Stochastic Processes. Random processes indexed by time: Markov chains, Lévy, and Gaussian processes.
Foundations and canonical references
The standard treatments of stochastic processes approach the subject from complementary angles. Lawler, Introduction to Stochastic Processes (2006) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Ross, Stochastic Processes (1996) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for stochastic processes include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2006Introduction to Stochastic Processeslawler-2006
- textbook · primary · 1996Stochastic Processesross-1996
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Explore
- 01
Markov Chains
Discrete- and continuous-time chains, stationarity, mixing, and coupling.
- 02
Mixing Times of Markov Chains
Spectral gap, conductance, and cutoff phenomena.
- 03
Brownian Motion
Wiener process, sample-path regularity, and martingale characterization.
- 04
Lévy Processes
Independent-increment processes, Poisson, jump diffusions.
- 05
Gaussian Processes
Covariance kernels, regularity, and supremum bounds.
- 06
Branching Processes
Galton–Watson, multitype branching, and superprocesses.
- 07
Random Walks
Simple and biased walks, hitting times, and Green's functions.
- 08
Point Processes
Poisson, Cox, Hawkes, and determinantal processes.
- 09
Interacting Particle Systems
Contact processes, exclusion processes, and voter models.
Review this topic
This page was drafted by an agent and is waiting on expert review. Spotted a wrong prerequisite, a missing concept, a misattributed source, or a factual slip? Tell us — your review opens a tracked issue maintainers act on.