@ARTICLE{Piwowarski_Wiesław_Mathematical_2000,
 author={Piwowarski, Wiesław},
 volume={vol. 49},
 number={No 1},
 journal={Geodesy and Cartography},
 pages={21-38},
 howpublished={online},
 year={2000},
 publisher={Commitee on Geodesy PAS},
 abstract={The paper presents the problem of determination of one- and multi-stage prognosis of post-mining surface dislocations. The finite and chronologically ordered vector of geodetic surveys is the describing variable herein. Completed surveys show that the analyzed process can be written as a composition of both deterministic process and singular one. Hence the quantitative description of the kinetics of the process of dislocation forming has been assigned to the class of the stochastic model. An adequate series sum in which time is the argument and random variables are the values makes up the formal definition of the model. The optimization of one-stage prognosis has been carried out for utility purposes. The Durbin-Levinson algorithm is the applied numerical procedure. The utility fragment of this is based on verification of the defined model for certain mining-geological conditions and surveying results. The obtained analytical representation and optimal prognosis of the kinetics of vertical dislocations correspondend to surveying results, which can be testified by adequate measures of the quality of description of the process.},
 type={Article},
 title={Mathematical modelling of post-mining dislocations kinetics as a quasi-random process},
 URL={http://journals.pan.pl/Content/121691/PDF-MASTER/5_GK_TOM_XLIX_ZESZYT_1_2000_Piwowarski_Modelowanie_matematyczne.pdf},
}