ISSN 2738-0971 | eISSN 2738-1013
Bulletin of Natural Sciences Research
Open access journal | Double-blind peer review

Dragana Valjarević

University of Pristina, Faculty of Natural Sciences and Mathematics, Kosovska Mitrovica

Articles

Open Access Original Scientific Paper

STATISTICAL CAUSALITY AND QUASIMARTINGALES

by Dragana Valjarević, Ljiljana Petrović

Concept of causality is very popular and applicable nowadays, especially when we consider the cases "what would happen if" and "what would have happened if". Here we consider the concept of causality based on the Granger’s definition of causality, introduced in Mykland (1986). Many of the systems to which it is natural to apply tests of causality take place in continuous time, so we will consider the continuous time processes. Here we consider the connection between the concept of causality and the property of being a quasimartingale. Quasimartingales were investigated by Fisk (1965), Orey and specially Rao (1969). Namely, in this paper we prove an equivalence between the given concept of causality and preservation of quasimartingale property if the filtration is getting larger. We prove the same equivalence for the stopped quasimartingale with respect to the truncated filtrations.

View Full-Text DOI 10.5937/univtho8-18934 Published: 02 Dec 2018
Open Access Original Scientific Paper

CAN THE TRANSFORMATION OF INSTRUCTION PROCESS INTO A VIRTUAL PLACE INDUCE A SHIFT IN BEHAVIORAL PATTERNS OF TEACHERS AND STUDENTS?

by Eugen Ljajko, Vladica Stojanović, Dragana Valjarević, Tanja Jovanović

The goal of this study is to reveal possible influence that the participants’ age and Information and Communications Technologies (ICT) usage in the instruction process can have on behavior that defines whether students and teachers belong to one of the Digital Native/Immigrant or Visitor/Resident groups. We collected data through two surveys that covered a total of 1273 students and 382 teachers from southern regions of Serbia. The surveys consisted of questions about availability of computers and internet, ICT use in the instruction process, and communication habits in the ICT-empowered instruction process. The first survey covered both, students and teachers that were involved in the instruction process mostly deprived of the ICT usage. The second survey covered participants of an instruction process that was successfully improved by an ICT usage. Data analysis shows a shift in communication patterns of teachers and a sharp improvement in computer use for educational purposes for both groups included in the surveys. The change is induced by a proper ICT usage in the instruction process. Conclusions that followed the data analysis lead us to better approaches in organizing ICT usage in the instruction process that enable participants fully employ their resources in order to improve teaching techniques and learning.

View Full-Text DOI 10.5937/univtho6-11953 Published: 31 Dec 2016
Open Access Original Scientific Paper

CONCEPT OF STATISTICAL CAUSALITY AND LOCAL MARTINGALES

by Dragana Valjarević, Ljiljana Petrović

In this paper we consider a statistical concept of causality in continuous time in filtered probability spaces which is based on Granger's definitions of causality. The given causality concept is closely connected to the preservation of the property being a local martingale if the filtration is getting larger. Namely, the local martingale remains unpredictable if the amount of information is increased. We proved that the preservation of this property is equivalent with the concept of causality.

View Full-Text DOI 10.5937/univtho6-10968 Published: 03 Aug 2016