On the Markov processes of Schrödinger, the Feynman-Kac formula and stochastic control. (English) Zbl 0726.60066
Realization and modelling in system theory, Proc. Int. Symp., Math. Theory Networks Syst., MTNS, Vol. I, Amsterdam/Neth. 1989, Prog. Syst. Control Theory 3, 497-504 (1990).
Summary: [For the entire collection see Zbl 0723.00046.]
We give a stochastic control formulation of a problem considered by E. Schrödinger [Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl. H. 8/9, 144-153 (1931; Zbl 0001.37503)]. In passing, we get a quick proof of the Feynman-Kac formula relying on a Girsanov transformation. We also discuss the connections to the work of Jamison on reciprocal processes, and to the work of Fleming, Mitter, Sheu, Zambrini and Guerra on the logarithmic transformation.
We give a stochastic control formulation of a problem considered by E. Schrödinger [Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl. H. 8/9, 144-153 (1931; Zbl 0001.37503)]. In passing, we get a quick proof of the Feynman-Kac formula relying on a Girsanov transformation. We also discuss the connections to the work of Jamison on reciprocal processes, and to the work of Fleming, Mitter, Sheu, Zambrini and Guerra on the logarithmic transformation.
MSC:
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
| 93E20 | Optimal stochastic control |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
