creator Albert, Hannah advisor Li, Xiaofan The mean exit time and transition probability density function are macroscopic quantities used to determine the behavior of stochastic di↵erential equations (SDEs). The integral-di↵erential equations determining these quantities for SDEs with non- Gaussian ↵-stable L´evy motions involve a nonlocal term consisting of a singular integral, which is a manifestation of the ’flights’ or ’jumps’ due to the non-Gaussian noise. A two-dimensional SDE with radially symmetric ↵-stable L´evy motion is considered, and an efficient second-order accurate numerical scheme is developed for calculating the mean exit time and transition probability density function. The scheme is numerically verified by testing the results of the deterministic integral-di↵erential equations with a known, smooth function u(x) in place of themean exit time, and by calculating an unknown mean exit time u(x). Submitted by Erma Thomas (thomase@iit.edu) on 2016-07-18T21:21:10Z No. of bitstreams: 1 etdadmin_upload_424505.zip: 4536913 bytes, checksum: 66c6f784cbc89fd09eaee0fe92af88da (MD5) Made available in DSpace on 2016-07-18T21:21:10Z (GMT). No. of bitstreams: 1 etdadmin_upload_424505.zip: 4536913 bytes, checksum: 66c6f784cbc89fd09eaee0fe92af88da (MD5) Previous issue date: 2016-05 M.S. in Applied Mathematics, May 2016 2016 2016-05 http://hdl.handle.net/10560/3872 en integro-differential equation Lévy motion mean exit time stochastic differential equation Stochastic dynamical systems Thesis born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department