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Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian
Embedding Riemannian Manifolds Heat Kernel Connection Laplacian
2013/6/17
Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associa...
Invariant measures for stochastic heat equations
Invariant measures stochastic heat equations
2009/9/22
The paper is concerned with the asymptotic behaviour
of solutions to the nonlinear stochastic heat equations, with spatially
homogeneous noise, in the whole space. Sufficient conditions for the
exi...
The Stochastic Heat Equation with Fractional-Colored Noise:Existence of the Solution
Stochastic heat equation Gaussian noise stochastic integral fractional Brownian motion spatial covariance function
2009/6/12
The Stochastic Heat Equation with Fractional-Colored Noise:Existence of the Solution.
Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
Hitting probabilities systems of non-linear stochastic heat equations space-time white noise capacity Hausdor measure
2009/6/12
We consider a system of d coupled non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional additive space-time whitenoise. We establish upper and lower bounds on hitting pro...
Some Remarks on the Heat Flow for Functions and Forms
Heat semigroup heat equation Brownian motion damped parallel translation Ricci curvature
2009/5/8
This note is concerned with the differentiation of heat semigroups on Riemannian manifolds. In particular, the relation $dP_tf=P_tdf$ is investigated for the semigroup generated by the Laplacian with ...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
heat equation white noise stochastic partial differential equations
2009/4/29
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...
On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise
Coalesce duality entrance law Fisher-Wright noise particle system
2009/4/24
This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
stochastic fractional Brownian motion
2009/4/22
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...
On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise
Duality Brownian Particles Heat Equation Fisher-Wright Noise
2009/4/7
This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the...