Abstract: Mathematical proofs when written in conventional ways often contain imprecise definitions, unstated background assumptions, and inferential gaps in reasoning.

Abstract:  In this thesis, we develop computational algorithms in a number of different regimes for pricing financial American options.

Change of measure techniques are ubiquitous in many areas of applied probability including in model selection in finance and in efficient simulation of rare events.

In this talk, we discuss three problems. The first is on an asynchronous multi-antenna wireless communication system and the later two are on collaborative estimation.