This research investigates existing relationships between the three apparently unrelated
subjects: Markov process, Semigroups and Partial difierential equations.
Markov processes define semigroups through their transition functions. Conversely
particular semigroups determine transition functions and can be regarded as Markov
processes. We have exploited these relationships to study some Markov chains.
The infnitesimal generator of a Feller semigroup on the closure of a bounded domain
of Rn; (n ^ 2), is an integro-diferential operator in the interior of the domain and verifes
a boundary condition.
The existence of a Feller semigroup defined by a diferential operator and a boundary
condition is due to the existence of solution of a bounded value problem. From this result
other existence suficient conditions on the existence of Feller semigroups have been
obtained and we have applied some of them to construct Feller semigroups on the unity
disk of R2.Decision SciencesM. Sc. (Operations Research
