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Mathematics Colloquium – Dr. David Lipshutz

Author: las-digital

Sensitivity analysis of reflected diffusions

Reflected diffusions (RDs) constrained to remain in convex polyhedral domains arise in a variety
of contexts, including as “heavy traffic” limits of queueing networks and in the study of rankbased
interacting particle models. Sensitivity analysis of such an RD with respect to its defining
parameters is of interest from both theoretical and applied perspectives. In this talk I will
characterize pathwise derivatives of an RD in terms of solutions to a linear constrained stochastic
differential equation whose coefficients, domain and directions of reflection depend on the state
of the RD. I will demonstrate how pathwise derivatives are useful in Monte Carlo methods to
estimate sensitivities of an RD, and also in characterizing sensitivities of the stationary
distribution of an RD. The proofs of these results involve a careful analysis of sample path
properties of RDs, as well as geometric properties of the convex polyhedral domain and the
associated directions of reflection along its boundary.