Strong p-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds

Li, Xue Mei

doi:10.1007/bf01268991

Cited by 69 publications

(99 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The precise statement is given in Remark B.9 below. Similar discussions may be found in Bru ning and Lesch [7], Xue-Mei Li [40,41] and in Bueler [8]. Remark B.9.…”

Section: B2 a Commutativity Resultssupporting

confidence: 60%

Heat Equation Derivative Formulas for Vector Bundles

Driver

Thalmaier

2001

Journal of Functional Analysis

View full text Add to dashboard Cite

We use martingale methods to give Bismut type derivative formulas for differentials and co-differentials of heat semigroups on forms, and more generally for sections of vector bundles. The formulas are mainly in terms of Weitzenbo ck curvature terms; in most cases derivatives of the curvature are not involved. In particular, our results improve B. K. Driver's formula in (1997, J. Math. Pures Appl. (9) 76, 703 737) for logarithmic derivatives of the heat kernel measure on a Riemannian manifold. Our formulas also include the formulas of K. D. Elworthy and X.-M. Li (1998, C. R. Acad. Sci. Paris Se r. I Math. 327, 87 92). Academic Press

show abstract

“…The precise statement is given in Remark B.9 below. Similar discussions may be found in Bru ning and Lesch [7], Xue-Mei Li [40,41] and in Bueler [8]. Remark B.9.…”

Section: B2 a Commutativity Resultssupporting

confidence: 60%

Heat Equation Derivative Formulas for Vector Bundles

Driver

Thalmaier

2001

Journal of Functional Analysis

View full text Add to dashboard Cite

show abstract

“…is said to be strongly p-complete, for 1 ≤ p ≤ n, if {X x t } is jointly continuous in time and space for all time when restricted to a smooth p-simplex. See [12]. Roughly speaking strong p-completeness means the flow sends a C r−1 p-dimensional submanifold to a C r−1 submanifold.…”

Section: A Non-integrability Results For General Diffusionsmentioning

confidence: 99%

“…In particular there is no explosion if (59) holds for p = 1 (and under somewhat weaker conditions [12]). For example consider dX t = dB t on 1 n −{0} for {B t } an n-dimensional Brownian motion starting from 0.…”

Section: A Non-integrability Results For General Diffusionsmentioning

confidence: 99%

The importance of strictly local martingales; applications to radial Ornstein–Uhlenbeck processes

Elworthy¹,

Li²,

Yor

1999

Probab Theory Relat Fields

Self Cite

View full text Add to dashboard Cite

For a wide class of local martingales (M t ) there is a default function, which is not identically zero only when (M t ) is strictly local, i.e. not a true martingale. This 'default' in the martingale property allows us to characterize the integrability of functions of sup s≤t M s in terms of the integrability of the function itself. We describe some (paradoxical) mean-decreasing local sub-martingales, and the default functions for Bessel processes and radial Ornstein-Uhlenbeck processes in relation to their first hitting and last exit times. Classification (1991): 60G44, 60J60, 60H15 Mathematics Subject

show abstract

“…Remark 1 and is valid for any potential which satisfies conditions (27), (30), (31) The proof of the theorem will be given in the next section. In what follows, we will always assume that the conditions (30)- (31) hold.…”

Section: Theoremmentioning

confidence: 99%

Random Witten Laplacians: traces of semigroups, $L^2$-Betti numbers and index

Albeverio¹,

Daletskii²,

Kalyuzhnyi³

2008

J. Eur. Math. Soc.

View full text Add to dashboard Cite

Abstract. Random Witten Laplacians on infinite coverings of compact manifolds are considered. The probabilistic representations of the corresponding heat kernels are given. The finiteness of the von Neumann traces of the corresponding semigroups is proved, and the short-time asymptotics of the corresponding supertrace is computed. Examples associated with Gibbs measures on configuration spaces and product manifolds are considered.

show abstract

Strong p-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds

Cited by 69 publications

References 16 publications

Heat Equation Derivative Formulas for Vector Bundles

Heat Equation Derivative Formulas for Vector Bundles

The importance of strictly local martingales; applications to radial Ornstein–Uhlenbeck processes

Random Witten Laplacians: traces of semigroups, $L^2$-Betti numbers and index

Contact Info

Product

Resources

About