We show that relative entropy decreases for continuous time Markov chains.
We explain why certain distributions arise naturally as the limit of coin throws.
- Bernoulli, Binomial Distributions, Geometric Distributions.
- Binomial to Poisson Distribution; Geometric to Exponential; Binomial to Normal.
We consider a system consisting of interacting objects. As we let the number of objects increase, we can characterize the limiting behaviour of the system.
Lyapunov functions are an extremely convenient device for proving that a dynamical system converges.
For a number of differing auction settings, we consider the sale of a single item amongst fixed number of auction participants. It is interesting that under a certain game-theoretic construction all these auctions can be seen to be equivalent.
In the Cross Entropy Method, we wish to estimate the likelihood
Here is a random variable whose distribution is known and belongs to a parametrized family of densities . Further is often a solution to an optimization problem.
We consider the setting of sequentially optimizing the average of a sequence of functions, so called online convex optimization.