Burkill's integrals dependent on a parameter

Uniform Decay and Equicontinuity for Normalized, Parameter Dependent, Ito Integrals

Dependent, Ito Integrals David Levanony, Adam Shwartz and Ofer Zeitouni Department of Electrical Engineering Technion Israel Institute of Technology Haifa 32000, Israel Abstract Let fMt( ); t 0g 2IRd be a collection of continuous, continuous-time martingales such that for all t > 0, the associated increasing processes satisfy < M( ) >t!1 as k k ! 1. We show that if < M( ) >t grows with k k su c...

Feynman parameter integrals

We often deal with products of many propagator factors in loop integrals. The trick is to combine many propagators into a single fraction so that the four-momentum integration can be done easily. This is done commonly using so-called Feynman parameters. We rewrite the product of propagators 1 (A 1 + ii)(A 2 + ii) · · · (A n + ii) , (1) where A i has the form of p 2 − m 2. The sign of A i is not...

Multi-parameter singular integrals

Multiple integrals: Lagrangian Dependent on several minimizers

Universal Integrals Based on Level Dependent Capacities

Three different types of universal integral based on level dependent capacities are introduced and discussed. Two extremal types are based on Caratheodory’s idea of inner and outer measures, while the third type is introduced for copula-based universal integrals only. Keywords—Choquet integral, Copula, Fuzzy measure, Level dependent capacities, Sugeno integral, Universal integral.