Limits of random differential equations on manifolds
File(s)
Accepted version
Author(s)
Li, X-M
Type
Journal Article
Abstract
Consider a family of random ordinary differential equations on a manifold
driven by vector fields of the form
k Ykαk (z
t (ω)) where Yk are vector fields, is
a positive number, z
t is a 1
L0 diffusion process taking values in possibly a different
manifold, αk are annihilators of ker(L∗
0). Under Hörmander type conditions on L0 we
prove that, as approaches zero, the stochastic processes y
t
converge weakly and in
the Wasserstein topologies. We describe this limit and give an upper bound for the rate
of the convergence.
driven by vector fields of the form
k Ykαk (z
t (ω)) where Yk are vector fields, is
a positive number, z
t is a 1
L0 diffusion process taking values in possibly a different
manifold, αk are annihilators of ker(L∗
0). Under Hörmander type conditions on L0 we
prove that, as approaches zero, the stochastic processes y
t
converge weakly and in
the Wasserstein topologies. We describe this limit and give an upper bound for the rate
of the convergence.
Date Issued
2016-12-01
Date Acceptance
2015-09-15
Citation
Probability Theory and Related Fields, 2016, 166 (3-4), pp.659-712
ISSN
0178-8051
Publisher
Springer
Start Page
659
End Page
712
Journal / Book Title
Probability Theory and Related Fields
Volume
166
Issue
3-4
Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00440-015-0669-x
Identifier
http://dx.doi.org/10.1007/s00440-015-0669-x
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
COLLAPSING RIEMANNIAN-MANIFOLDS
RANDOM EVOLUTIONS
THEOREM
CONVERGENCE
PRINCIPLE
SYSTEMS
FLOWS
LAWS
math.PR
math.PR
0101 Pure Mathematics
0102 Applied Mathematics
0104 Statistics
Statistics & Probability
Notes
mrclass: 60H25 (34F05 58J65 60B10 60F05 60H10 60J60) mrnumber: 3568037
Publication Status
Published
Date Publish Online
2015-10-01