Тип публикации: научное издание
Год издания: 2013
Идентификатор DOI: 10.1515/9783110288537.73
Ключевые слова: asymptotic expansion, Epidemic Equation, evolution equation, Repre-sentation of Solution, series solution
Аннотация: Markov stochastic processes give rise to evolution equations of the formPuDAu,whereAis a stationary differential operator with polynomial coefficients.The unknown functionuis the probability generating function of the process, and soit takes the values in bounded holomorphic functions on the unit polydisk inCn.Asbut one example of Показать полностьюsuch equations we study in this paper the epidemic equation. Wederive an explicit formula for the formal power series solution of epidemic equationunder initial conditions. For general equationsPuDAuwe discuss the solvabilityquestion under initial conditionu.0/Du0with data in holomorphic functions on theunit polydisk.
Журнал: Mathematics and Life Sciences
Выпуск журнала: 1
Номера страниц: 71-86
Место издания: Berlin, Boston
Издатель: Walter de Gruyter GmbH & Co. KG