Abstract.
Ito's rule is established for the diffusion processes on the graphs. We also consider a family of diffusions processes with small noise on a graph. Large deviation principle is proved for these diffusion processes and their local times at the vertices.
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Received: 12 February 1997 / Revised version: 3 March 1999
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Freidlin, M., Sheu, SJ. Diffusion processes on graphs: stochastic differential equations, large deviation principle. Probab Theory Relat Fields 116, 181–220 (2000). https://doi.org/10.1007/PL00008726
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DOI: https://doi.org/10.1007/PL00008726
- Mathematics Subject Classification (1991): Primary 60J60; Secondary 60H10, 60J55, 60F10
- Key words and phrases: Diffusions on graphs – Local time – Small random perturbation – Large deviations