Order Preservation for Path-Distribution Dependent SDEs

Abstract

Sufficient and necessary conditions are presented for the order preservation of path-distribution dependent SDEs. Differently from the corresponding study of distribution independent SDEs, to investigate the necessity of order preservation for the present model we need to construct a family of probability spaces in terms of the ordered pair of initial distributions.

12 pages

References in corpus (1)

• Nonlinear Fokker-Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs

Cited by in corpus (1)

• Least squares estimation for path-distribution dependent stochastic differential equations