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First‐passage densities of controlled Gaussian processes
Author(s) -
Lefebvre Mario
Publication year - 1989
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315527
Subject(s) - hitting time , probability density function , moment (physics) , moment generating function , gaussian , mathematics , stopping time , boundary (topology) , first hitting time model , function (biology) , invariant (physics) , gaussian process , statistical physics , mathematical analysis , physics , statistics , classical mechanics , mathematical physics , evolutionary biology , quantum mechanics , biology
Whittle has proved a theorem that gives the optimal control of Gaussian processes in terms of the mathematical expectation of a function of the time and the place where the uncontrolled processes hit the boundary of the stopping region for the first time. In this paper we obtain formulae for the joint probability density function of the first hitting time and place and, in the time‐invariant case, for the moment generating function of the first exit time of the optimally controlled processes. Two particular one‐dimensional cases are considered.