Mathematics – Probability
Scientific paper
Oct 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980apj...241..334k&link_type=abstract
Astrophysical Journal, Part 1, vol. 241, Oct. 1, 1980, p. 334-342.
Mathematics
Probability
2
Celestial Mechanics, Integral Equations, Stellar Motions, Stellar Systems, Dynamic Models
Scientific paper
The mathematical properties of integral master equations that are relevant to applications in stellar dynamics are discussed. The standard analysis of a master equation for a system with discrete states is extended first to systems characterized by a continuous variable and then to modified 'open' systems from which loss can occur. The ordinary master equation conserves probability, whereas the modified master equation guarantees loss for a system. The ordinary master equation has a unique asymptotically stable stationary solution. If this stationary solution obeys an equation of detailed balance, both the master and modified master equations admit self-adjoint formulations.
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