Affine diffusions with non-canonical state space

2010/04/03 by Peter Spreij, Spreij, Peter, Enno Veerman +1 · 1 citation
Mathematics · #60J60 #91G30 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J60 #msc:91G30

paper · pdf · doi:10.48550/arxiv.1004.0429

36 pages; paper is split into two papers; results on invariance and strong solutions added

arxiv created 2010/05/06 · arxiv updated 2010/05/10

Abstract

Multidimensional affine diffusions have been studied in detail for the case of a canonical state space. We present results for general state spaces and provide a complete characterization of all possible affine diffusions with polyhedral and quadratic state space. We give necessary and sufficient conditions on the behavior of drift and diffusion on the boundary of the state space in order to obtain invariance and to prove strong existence and uniqueness.

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• Weak solutions of Stochastic Volterra Equations in convex domains with general kernels

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