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91
Gaussian Upper Bounds For The Heat Kernel On Arbitrary Manifolds
, 1997
"... In this paper, we develop a universal way of obtaining Gaussian upper bounds of the heat kernel on Riemannian manifolds. By the word "Gaussian" we mean those estimates which contain a Gaussian exponential factor similar to one which enters the explicit formula for the heat kernel of the co ..."
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Cited by 63 (2 self)
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In this paper, we develop a universal way of obtaining Gaussian upper bounds of the heat kernel on Riemannian manifolds. By the word "Gaussian" we mean those estimates which contain a Gaussian exponential factor similar to one which enters the explicit formula for the heat kernel of the conventional Laplace operator in R...
SubGaussian estimates of heat kernels on infinite graphs
 Duke Math. J
, 2000
"... We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay. ..."
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Cited by 54 (10 self)
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We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.
A scheme for simulating onedimensional diffusion processes with discontinuous coefficients
 ANN. APPL. PROBAB
, 2006
"... The aim of this article is to provide a scheme for simulating diffusion processes evolving in onedimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of t ..."
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Cited by 32 (15 self)
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The aim of this article is to provide a scheme for simulating diffusion processes evolving in onedimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the points of discontinuity. This description is supplied with the local comparison of the trajectories of the diffusion processes with those of a skew Brownian motion.
Ondiagonal lower bounds for heat kernels and Markov chains
 Duke Math. J
, 1997
"... Let M be a Riemannian manifold, and ∆ be the LaplaceBeltrami operator on M. It is known that there exists a unique minimal positive fundamental solution to the associated heat equation, which is referred to as the heat kernel and denoted by pt(x, y) (x, y ∈ M, t> 0). ..."
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Cited by 24 (2 self)
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Let M be a Riemannian manifold, and ∆ be the LaplaceBeltrami operator on M. It is known that there exists a unique minimal positive fundamental solution to the associated heat equation, which is referred to as the heat kernel and denoted by pt(x, y) (x, y ∈ M, t> 0).
Boundary Harnack principle for Brownian motions with measurevalued drifts in bounded Lipschitz domains
 MATHEMATISCHE ANNALEN
, 2007
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Quantitative estimates of unique continuation for parabolic equations, determination of unknown timevarying boundaries and optimal stability estimates
, 2007
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Pointwise estimates for transition probabilities of random walks in infinite graphs
 in: Trends in mathematics: Fractals in Graz 2001
, 2002
"... walks on infinite graphs ..."
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