Stochastic processes and fields
Probabilistic structures over index sets and state spaces
2014-08-05 — 2017-06-15
Wherein a compendium of stochastic processes is presented, and attention is directed to martingales and Brownian motion as guiding examples, with links to proofs and explanatory essays provided.
probability
stochastic processes
time series
I might put some content here, when time permits, with particular reference to specific concepts I use.
- Martingales
- concentration properties
- Gaussian processes
- Branching processes
- Lévy processes
- Filtrations
- Mixing time characterisations
- Stochastic DEs
- General probability
- Stochastic independence
- Stochastic convolutions
- processes on manifolds
- …
1 Great explainers of stochastic processes
- Cosma Shalizi and Aryeh Kontorovich: Almost None of the Theory of Stochastic Processes
- Terry Tao as usual explains beautifully and unconventionally e.g. Brownian motion
- George Lowther has a blog full of nice tricks and painstaking explanation of ’em, e.g. Properties of the stochastic integral
- Dominic Yeo has a steady explanatory cadence e.g. Properties of the stochastic integral
- Djalil Chafaï has excellent plain-talk introductions to fresh probability.