# On minimax sequential procedures for exponential families of stochastic processes

Applicationes Mathematicae (1998)

- Volume: 25, Issue: 1, page 1-18
- ISSN: 1233-7234

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topMagiera, Ryszard. "On minimax sequential procedures for exponential families of stochastic processes." Applicationes Mathematicae 25.1 (1998): 1-18. <http://eudml.org/doc/219192>.

@article{Magiera1998,

abstract = {The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of diffusions, for estimating the mean or drift coefficients of the class of Ornstein-Uhlenbeck processes, for estimating the drift of a geometric Brownian motion and for estimating a parameter of a family of counting processes. A class of minimax sequential rules for a compound Poisson process with multinomial jumps is also found.},

author = {Magiera, Ryszard},

journal = {Applicationes Mathematicae},

keywords = {Bayes sequential estimation; minimax sequential procedure; exponential family of processes; stopping time; sequential decision procedure; sequential decision; minimax sequential estimation; exponential families of diffusions; Ornstein-Uhlenbeck processes; counting processes; compound Poisson process},

language = {eng},

number = {1},

pages = {1-18},

title = {On minimax sequential procedures for exponential families of stochastic processes},

url = {http://eudml.org/doc/219192},

volume = {25},

year = {1998},

}

TY - JOUR

AU - Magiera, Ryszard

TI - On minimax sequential procedures for exponential families of stochastic processes

JO - Applicationes Mathematicae

PY - 1998

VL - 25

IS - 1

SP - 1

EP - 18

AB - The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of diffusions, for estimating the mean or drift coefficients of the class of Ornstein-Uhlenbeck processes, for estimating the drift of a geometric Brownian motion and for estimating a parameter of a family of counting processes. A class of minimax sequential rules for a compound Poisson process with multinomial jumps is also found.

LA - eng

KW - Bayes sequential estimation; minimax sequential procedure; exponential family of processes; stopping time; sequential decision procedure; sequential decision; minimax sequential estimation; exponential families of diffusions; Ornstein-Uhlenbeck processes; counting processes; compound Poisson process

UR - http://eudml.org/doc/219192

ER -

## References

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