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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

9 votes
4 answers
3k views

How can the Kalman filter be adapted to handle binary observations?

Imagine a coin with a time-varying probability of coming up heads. (For example, perhaps the probability follows a random walk that is constrained to live in $[0, 1]$. And say we have some informati …
5 votes
1 answer
3k views

Between arithmetic and geometric Brownian motions: when are negative values possible?

Please note edits after original post changing the specific form of the setup Let's say we have a stochastic differential equation: $$ \mathrm{d}S_t = |S^\beta| {(\mu \mathrm{d}t + \sigma\mathrm{d}W_ …