Complex Probability and Markov Stochastic Process

Bijan Bidabad; Behrouz Bidabad

doi:10.46281/ijfb.v3i1.290

Bijan Bidabad Professor, Economics and Chief Islamic Banking Advisior, Bank Melli, Iran
Behrouz Bidabad Faculty of Mathematics, Polytechnics University, Hafez Ave., Tehran, 15914, Iran

DOI: https://doi.org/10.46281/ijfb.v3i1.290

Keywords: Prbability, Markov Process, Stochastic Process, Population Census

Abstract

This note discusses the existence of "complex probability" in the real world sensible problems. By defining a measure more general than the conventional definition of probability, the transition probability matrix of discrete Markov chain is broken to the periods shorter than a complete step of the transition. In this regard, the complex probability is implied.

References

R. Bellman (1970), Introduction to matrix analysis, McGraw–Hill.

P.J. Dhrymes (1978), Mathematics for econometrics. Springer-Verlag.

W. Feller (1970, 1971), An Introduction to probability theory and its applications, Vols. 1,2, Wiley, New York.

P.G. Hoel, S.C. Port, C. J. Stone (1972), Introduction to stochastic processes. Houghton Mifflin, New York.

S. Karlin, H.M.Taylor (1975), A first course in stochastic processes. Academic Press.

E. Klein (1973), Mathematical methods in theoretical economics, topological and vector space foundations of equilibrium analysis, Academic Press.

K.V. Mardia, J.T. Kent, J.M. Bibby (1982), Multivariate analysis, Academic Press.

H. Nikaido (1970), Introduction to sets and mapping in modern economics. North Holland Publishing Co.

S.S. Searle (1982), Matrix algebra useful for statistics. Wiley.

A.Takayama (1974) Mathematical economics. Dryden Press, Illinois.

E. Wentzel, L. Ovcharov (1986) Applied problems in probability theory. Mir, Moscow.