Journal of Functional Analysis

1993

DOI: 10.1006/jfan.1993.1145

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Stochastic Analysis on the Path Space of a Riemannian Manifold

Paul Malliavin²

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Transferring the Results To A Geometric Setting1

Integration By Part For the Regularized Metric1

Cairoli Equation and Brownian Sheet1

Introduction1

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Cited by 97 publications

(66 citation statements)

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“…also [5,6]. Finally for h ∈ H, t ∈ R, s ∈ [0, 1],γ ∈ P m 0 , and σ being the solution to the geometric flow equation (see [4], [9], [8])…”

Section: Transferring the Results To A Geometric Settingmentioning

confidence: 99%

A class of infinite dimensional stochastic processes with unbounded diffusion

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2015

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The paper studies Dirichlet forms on the classical Wiener space and the Wiener space over non-compact complete Riemannian manifolds. The diffusion operator is almost everywhere an unbounded operator on the Cameron-Martin space. In particular, it is shown that under a class of changes of the reference measure, quasi-regularity of the form is preserved.We also show that under these changes of the reference measure, derivative and divergence are closable with certain closable inverses. We first treat the case of the classical Wiener space and then we transfer the results to the Wiener space over a Riemannian manifold.

“…also [5,6]. Finally for h ∈ H, t ∈ R, s ∈ [0, 1],γ ∈ P m 0 , and σ being the solution to the geometric flow equation (see [4], [9], [8])…”

Section: Transferring the Results To A Geometric Settingmentioning

confidence: 99%

A class of infinite dimensional stochastic processes with unbounded diffusion

¹

,

²

2015

View full text Add to dashboard Cite

The paper studies Dirichlet forms on the classical Wiener space and the Wiener space over non-compact complete Riemannian manifolds. The diffusion operator is almost everywhere an unbounded operator on the Cameron-Martin space. In particular, it is shown that under a class of changes of the reference measure, quasi-regularity of the form is preserved.We also show that under these changes of the reference measure, derivative and divergence are closable with certain closable inverses. We first treat the case of the classical Wiener space and then we transfer the results to the Wiener space over a Riemannian manifold.

“…We follow [12]; an infinitesimal euclidean motion of the G ρ -cylindrical Brownian motion is defined…”

Section: Integration By Part For the Regularized Metricmentioning

confidence: 99%

Itô Atlas, its Application to Mathematical Finance and to Exponentiation of Infinite Dimensional Lie Algebras

2007

Stochastic Analysis and Applications

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No abstract

“…)(ǫ) ∈ A}, we can replace formally ǫB(.) by h with the formal measure (38). We refer to [16,114] for improvements of this theorem.…”

Section: Cairoli Equation and Brownian Sheetmentioning

confidence: 99%

The geometry of Brownian surfaces

2006

Probab. Surveys

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Motivated by Segal's axiom of conformal field theory, we do a survey on geometrical random fields. We do a history of continuous random fields in order to arrive at a field theoretical analog of Klauder's quantization in Hamiltonian quantum mechanic by using infinite dimensional Airault-Malliavin Brownian motion.

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