Parameter Estimation in Fractional Diffusion Models

Prof. Kęstutis Kubilius received his Ph.D. in mathematics at Vilnius University in 1981. Currently he is a professor of mathematics at the same university. His research work mainly focuses on limit theorems for semimartingales, theory of stochastic differential equations, and parameter estimation for fractional diffusion processes. He is the  author of more than 50 published papers.Prof. Yuliya Mishura received her Ph.D. in probability and statistics at Kyiv University in 1978 and received her postdoctoral degree in probability and statistics (habilitation) in 1990. She is currently a professor at Taras Shevchenko National University of Kyiv. She is the author of more than 250 research papers and 6 books. Her  research interests include theory and statistics of stochastic processes, fractional processes, stochastic analysis and financial mathematics.Dr. Kostiantyn Ralchenko is a postdoctoral researcher at the Department ofProbability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, where he also completed his Ph.D. in mathematics in 2012. His research interests include stochastic differential equations, fractional and multifractional processes, and statistics of stochastic processes. He is the author of 24 papers.

“The book presents various diffusion models with memory and provides effective methods for parameter estimation in these models. It may be interesting for researchers and practitioners, graduate and postgraduate students.” (Alex V. Kolnogorov, zbMATH 1388.60006, 2018)

• 1 Description and properties of the basic stochastic models.- 2 The Hurst index estimators for a fractional Brownian motion.- 3 Estimation of the Hurst index from the solution of a stochastic differential equation.- 4 Parameter estimation in the mixed models via power variations.- 5 Drift parameter estimation in diffusion and fractional diffusion models.- 6 The extended Orey index for Gaussian processes.- 7 Appendix A: Selected facts from mathematical and functional analysis.- 8 Appendix B: Selected facts from probability, stochastic processes and stochastic calculus.