Continuous-time models of generalized random walks
Date of Completion
Mathematics|Physics, Elementary Particles and High Energy
The Wiener process is the classical example of a mathematical model for Brownian movement. Wiener viewed Brownian movement essentially as a random walk: a Brownian particle's position at time t equals the sum of displacements over successive time intervals that partition [0, t]. This is a guideline to the definition of integrator. We can reverse the point of view and ask the following question: Under which (minimal) conditions is the process retrievable from its increments? ^ We present a construction (a blueprint) that is based on the application of multidimensional measure theory. This construction is extendible to processes indexed by n parameters. ^
Stricevic, Slaven, "Continuous-time models of generalized random walks" (2000). Doctoral Dissertations. AAI9982007.