Short-time Geometry of Random Heat Kernals Paperback / softback
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
This volume studies the behavior of the random heat kernel associated with the stochastic partial differential equation $du=\tfrac {1}{2} {\Delta}udt = (\sigma, \nabla u) \circ dW_t$, on some Riemannian manifold $M$.
Here $\Delta$ is the Laplace-Beltrami operator, $\sigma$ is some vector field on $M$, and $\nabla$ is the gradient operator.
Also, $W$ is a standard Wiener process and $\circ$ denotes Stratonovich integration.
The author gives short-time expansion of this heat kernel.
He finds that the dominant exponential term is classical and depends only on the Riemannian distance function.
The second exponential term is a work term and also has classical meaning.
There is also a third non-negligible exponential term which blows up.
The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields.
In the process, he develops a method to approximate the heat kernel to any arbitrary degree of precision.
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:bibliography
- Publisher:American Mathematical Society
- Publication Date:30/03/1998
- Category:
- ISBN:9780821806494
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:bibliography
- Publisher:American Mathematical Society
- Publication Date:30/03/1998
- Category:
- ISBN:9780821806494
