Closing the memory gap in stochastic functional differential equations

In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Campus Only Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2011

Author dc:creator

• Sancier-Barbosa, Flavia Cabral

Contributors dc:contributor

• Mohammed, Salah

• approximation scheme
• option pricing theory
• stochastic functional differential equations

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/346

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-1346