We consider a specific diffusion control problem. We focus on setting where there is one risky asset and one riskless asset, though we will see that much of the analysis passes over to multiple assets.
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.
Lyapunov functions are an extremely convenient device for proving that a dynamical system converges.