An introduction to the geometry of stochastic flows

By Fabrice Baudoin. 2004

169 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/4add6dad51568f3787f7354521096a15b3dd5d68

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Citations in the corpus

Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries (2011, background): “Let us recall (see for instance Chapter 3 in [11]) that the Ehresmann connection form α on O (M) is the unique skew-symmetric matrix α of one forms on O (M) such that: (1) α(X) = 0 if and only if X ∈ HO(M); (2) Vα(X) = X if and only if X ∈ VO(M), where HO(M) denotes the horizontal bundle and VO(M) t”
Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, unknown): “See [50, 7] for related point of views.”
Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry (2011, background): “A probabilistic approach to hypoelliptic diffusion equation can be found in [10, 18, 25], where the existence of a smooth heat kernel for such equations is given.”
Small time heat kernel asymptotics at the sub-Riemannian cut locus (2012, background): “The heat kernel on sub-Riemannian manifolds has been an object of attention starting from the late 70s [13, 15, 16, 18, 20, 25, 31, 37, 40, 53, 54], as have the geodesics and cut and conjugate loci of such manifolds [2, 3, 5, 8, 9, 24, 28, 42, 51].”
Parallel Transport and Functors (2007, background): “Besides, parallel transport along topological paths of bounded variation can be defined, and is of interest for its own right, see, for example, [Bau05].”
General Rough integration, Levy Rough paths and a Levy--Kintchine type formula (2012, background): “We note that Fawcett’s formula [3, 9, 29] for the expected value of iterated Stratonovich integrals of d-dimensional Brownian motion (with covariance matrix a = I in the aforementioned references)”
The subelliptic heat kernel on SU(2): representations, asymptotics and gradient bounds (2008, background): “More precisely from Mitchell theorem [23] (see also [7]), for any positive R: lim n→+∞ δGH (”
Euler estimates for rough differential equations (2006, background): “Remark 9 G ( R ) can be given a subriemannian structure so that the path t ∈ [0, 1] 7→ SN (γ )0,t is a subriemannian geodesic which connects the unit e with g ∈ G ( R ) , see [3, 18].”
On gradient bounds for the heat kernel on the Heisenberg group (2007, background): “We refer to [6] and [34] for such probabilistic aspects.”