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Schrödinger processes and large deviations. (English) Zbl 0736.60071

A large system of independent diffusing particles in which particles are killed at a certain space-time dependent rate is considered. In particular the conditional distribution of the surviving trajectories in a bounded time interval is computed, given the approximate form of the initial and final empirical distribution of surviving particles. The resulting distribution is characterized in terms of a minimum relative entropy criterion. This generalizes a result for the Brownian case without killing, which was first obtained by E. Schrödinger [Sitzungsber., Preuss. Akad. Wiss., Phys. Math. Kl. H. 8/9, 144-153 (1931; Zbl 0001.37503)].

MSC:

60J60 Diffusion processes

Citations:

Zbl 0001.37503
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References:

[1] DOI: 10.1007/BF00532864 · Zbl 0326.60033 · doi:10.1007/BF00532864
[2] DOI: 10.1007/BF00535844 · Zbl 0365.60064 · doi:10.1007/BF00535844
[3] DOI: 10.1007/BF00340014 · Zbl 0666.60073 · doi:10.1007/BF00340014
[4] DOI: 10.1063/1.528481 · Zbl 0692.60060 · doi:10.1063/1.528481
[5] DOI: 10.1063/1.527002 · Zbl 0623.60102 · doi:10.1063/1.527002
[6] DOI: 10.1214/aop/1176993227 · Zbl 0544.60011 · doi:10.1214/aop/1176993227
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