Divergence Theorems in Path Space
نویسنده
چکیده
We obtain divergence theorems on the solution space of an elliptic stochastic differential equation defined on a smooth compact finite-dimensional manifold M . The resulting divergences are expressed in terms of the Ricci curvature of M with respect to a natural metric on M induced by the stochastic differential equation. The proofs of the main theorems are based on the lifting method of Malliavin together with a fundamental idea of Driver.
منابع مشابه
Fixed point theorems under c-distance in ordered cone metric space
Recently, Cho et al. [Y. J. Cho, R. Saadati, S. H. Wang, Common xed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254-1260] dened the concept of the c-distance in a cone metric space and proved some xed point theorems on c-distance. In this paper, we prove some new xed point and common xed point theorems by using the distance in ordered con...
متن کاملFixed Point Theorems for kg- Contractive Mappings in a Complete Strong Fuzzy Metric Space
In this paper, we introduce a new class of contractive mappings in a fuzzy metric space and we present fixed point results for this class of maps.
متن کاملNon-Archimedean fuzzy metric spaces and Best proximity point theorems
In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...
متن کاملDivergence theorems in path space III: hypoelliptic diffusions and beyond∗
Let x denote a diffusion process defined on a closed compact manifold. In an earlier article, the author introduced a new approach to constructing admissible vector fields on the space of paths associated to x, under the assumption that x is elliptic. In this article, this method is extended to yield similar results for degenerate diffusion processes. In particular, these results apply to non-e...
متن کاملStability and convergence theorems of pointwise asymptotically nonexpansive random operator in Banach space
In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.
متن کامل