The Stochastic Analysis Method
This chapter deals with probabilistic methods of obtaining the heat kernel. The main idea of this subject is that the heat kernel can be represented as a transition density of an associated stochastic process, as pointed out by Kolmogorov  in the early 1930s. The probabilistic methods were also useful in obtaining the heat kernel of the Heisenberg Laplacian, as shown by Hulanicki  and Gaveau  in the late 1970s.
KeywordsBrownian Motion Stochastic Differential Equation Heat Kernel Transition Density Stochastic Analysis
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