Kalman filtering (and filtering in general) considers the following setting: we have a sequence of states , which evolves under random perturbations over time. Unfortunately we cannot observe , we can only observe some noisy function of , namely, . Our task is to find the best estimate of given our observations of . Continue reading “Kalman Filter”

# Category: Uncategorized

## Mixing Times

In loose terms, the mixing time is the amount of time to wait before you can expect a Markov chain to be close to its stationary distribution. We give an upper bound for this.

## Diffusion Control Problems

We consider a continuous time analogue of Markov Decision Processes.

## Notes for Stochastic Control 2019

The link below contains notes PDF for this years stochastic control course

I’ll upload individual posts for each section. I’ll likely update these notes and add more exercises over the coming semester. I’ll add this update in a further post at the end of the course. Comments, typos, suggestions are always welcome.

## Markov’s Inequality, Chebychev’s Inequality and the Weak Law of Large Numbers

## Probability Son, Father and Grandfather have same birthday.

Here is a quick request for comments for Probability 1 students. Here are two answers saying that the probability that a grandfather, father and son are all born on the same day.

https://www.mirror.co.uk/news/uk-news/baby-boy-born-same-date-13416140

https://www.bbc.co.uk/news/world-us-canada-41406855#

The first answer is sort of wrong because it assumes you specify in advance date of birth. The second answer is right because we assume in advance we are given three generations and we assume we deal with a first born son.

Please leave comments below and will forward them on to BBC.