dorsal/arxiv
View SchemaNonnegative Feynman-Kac Kernels in Schr\"{o}dinger's Interpolation Problem
| Authors | Ph. Blanchard, P. Garbaczewski, R. Olkiewicz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9507002 |
| URL | https://arxiv.org/abs/quant-ph/9507002 |
| DOI | 10.1063/1.532004 |
| Journal | J.Math.Phys. 38 (1997) 1-15 |
Abstract
The existing formulations of the Schr\"{o}dinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We extend the framework to encompass singular potentials and associated nonnegative Feynman-Kac-type kernels. It allows to deal with general nonnegative solutions of the Schr\"{o}dinger boundary data problem. The resulting stochastic processes are capable of both developing and destroying nodes (zeros) of probability densities in the course of their evolution.
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"abstract": "The existing formulations of the Schr\\\"{o}dinger interpolating dynamics,\nwhich is constrained by the prescribed input-output statistics data, utilize\nstrictly positive Feynman-Kac kernels. This implies that the related Markov\ndiffusion processes admit vanishing probability densities only at the\nboundaries of the spatial volume confining the process. We extend the framework\nto encompass singular potentials and associated nonnegative Feynman-Kac-type\nkernels. It allows to deal with general nonnegative solutions of the\nSchr\\\"{o}dinger boundary data problem. The resulting stochastic processes are\ncapable of both developing and destroying nodes (zeros) of probability\ndensities in the course of their evolution.",
"arxiv_id": "quant-ph/9507002",
"authors": [
"Ph. Blanchard",
"P. Garbaczewski",
"R. Olkiewicz"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.532004",
"journal_ref": "J.Math.Phys. 38 (1997) 1-15",
"title": "Nonnegative Feynman-Kac Kernels in Schr\\\"{o}dinger\u0027s Interpolation Problem",
"url": "https://arxiv.org/abs/quant-ph/9507002"
},
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