4cb66933-241d-45f7-be20-1b84367ea37920210802030930638wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SIGNAL PROCESSING2224-34881790-505210.37394/232014http://wseas.org/wseas/cms.action?id=4062331202133120211710.37394/232014.2021.17https://wseas.org/wseas/cms.action?id=23315On Stochastic Differential Equations Generating Non-gaussian Continuous Markov ProcessVladimirLyandresSchool of Electrical and Computer Engineering, Ben-Gurion University of the Negev P.O. Box 653, Beer-Sheva, 84105, ISRAELContinuous Markov processes widely used as a tool for modeling random phenomena in numerous applications, can be defined as solutions of generally nonlinear stochastic differential equations (SDEs) with certain drift and diffusion coefficients which together governs the processâ€™ probability density and correlation functions. Usually it is assumed that the diffusion coefficient does not depend on the process' current value. For presentation of non-Gaussian real processes this assumption becomes undesirable, leads generally to complexity of the correlation function estimation. We consider its analysis for the process with particular pairs of the drift and diffusion coefficients providing the given stationary probability distribution of the considered process82202182202165688https://wseas.com/journals/sp/2021/a165114-006(2021).pdf10.37394/232014.2021.17.8https://wseas.com/journals/sp/2021/a165114-006(2021).pdfHull W. J., Futures and other Derivatives, Pearson Education India, 2006. 10.1111/1467-9965.t01-1-00023Nicolato E., Venardos E., Option pricing in stochastic volatility models of e OrnsteinUhlenbeck type, Mathematical Finance, 13 (4) (2003) 445-466. 10.1098/rstb.2010.0078Smouse P. E., Focardi S., Moorcroft P. Kie J. G., Forester J. D., Morales J. M., Stochastic modelling of animal movement, Philosophical Transactions of the Royal Society B: Biological Sciences, 365 (1550) 2201-2211. Barucha-Reid A. T., Elements of the Theory of Markov Processes and their Applications, McGraw Hills, 1960. Lyandres V., Model of deep fading, Information and Control Systems, 1 (2018) 123- 127. Stratonovich. R. L., Topics in the Theory of Random Noise, Vol. 1, Gordon and Breach, 1967. 10.1016/b978-0-08-009306-2.50005-4Nakagami M., The m-distribution â€“ A general formula of intensity of rapid fading, Methods in Radio Wave Propagation, Pergamon, 1960. 10.1002/0470021187Primak S., Kontorovich V., Lyandres V, Stochastic Methods and their Applications to Communications. Stochastic Differential Equations Approach, Wiley, 2004. Gradshtein L., Ryzhik I., Tables of Integrals, Series, and Products, Academic Press, 2014. Zayezdny A., Tabak D., Wulich D., Engineering Applications of Stochastic Processes: Theory, Problems and Solutions, Research Studies Press, Tauton, Somerset, 1989.