3 citations · 5 across the 5 of their papers we have counts for
6 papers
Product Gauges for Product Domains
Pat Muldowney
In generalized Riemann integration (or Henstock-Kurzweil integration), the formation of the partitions used in Riemann sum construction is regulated by rules known as gauges. This…
Beyond Dominated Convergence: Newer Methods of Integration
Patrick Muldowney
Lebesgue's dominated convergence theorem is a crucial pillar of modern analysis, but there are certain areas of the subject where this theorem is deficient. Deeper criteria for con…
Ralph Henstock's Lectures on the Theory of Integration
Ralph Henstock, Pat Muldowney
These are the class notes of lectures given by Ralph Henstock at the New University of Ulster in 1970-71. The notes deal with the Riemann-complete integral (also known as the gener…
Pricing American and Asian Options
Pat Muldowney
An analytic method for pricing American call options is provided; followed by an empirical method for pricing Asian call options. The methodology is the pricing theory presented in…
Understanding stochastic differential equations
Pat Muldowney
This essay explores the meaning of stochastic differential equations and stochastic integrals. It sets these subjects in a context of Riemann-Stieltjes integration. It is intended…
The Generalized Riemann or Henstock Integral Underpinning Multivariate Data Analysis: Application to Faint Structure Finding in Price Processes
Pat Muldowney, Fionn Murtagh
Practical data analysis involves many implicit or explicit assumptions about the good behavior of the data, and excludes consideration of various potentially pathological or limit…