Statistics of Random Processes and Optimal Control

Festschrift Albert Shiryaev - 90 Years
Erscheinungsjahr 2027
ISBN: 978-3-032-26264-6
Verlag: Springer

Buch, Englisch, 766 Seiten, Format (B × H): 155 mm x 235 mm

In 2024, Professor Albert Shiryaev turned 90 and remains as active as ever. This Festschrift volume honours Professor Shiryaev’s remarkable academic career, marked by foundational breakthroughs in Probability Theory, Statistics of Random Processes, Sequential Analysis, Optimal Stopping Theory, and Mathematical Finance. A Distinguished Professor of Lomonosov Moscow State University and the Steklov Mathematical Institute, Albert Shiryaev is a leading and highly prolific scholar.

This volume brings together invited contributions from researchers who have either worked closely with Professor Shiryaev or whose work has been shaped by his ideas and scholarship. The contributions, encompassing diverse fields, reflect current progress driven by the continual development of novel stochastic techniques and methods.

Zielgruppe

Research

Autoren/Hrsg.

Kordzakhia, Nino

Chigansky, Pavel

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik
• Wirtschaftswissenschaften Wirtschaftswissenschaften Wirtschaftswissenschaften: Allgemeines

Inhaltsverzeichnis

 Part I. Stochastic Analysis and Its Applications in Mathematical Finance and Economics.- 1. Volatility Estimation from a View Point of Entropy (J. Akahori, R. Namba, and A.Watanabe).- 2. Stochastic models associated with nonlinear PDEs (Y. Belopolskaya).- 3. Asymptotic analysis in problems with fractional processes (P. Chigansky, and M. Kleptsyna).- 4. No arbitrage and the existence of ACLMMs in general diffusion models (D. Criens, and M. Urusov).- 5. On some regime switching diffusions and their applications ( M. L. Esqu´ivel, N.  P. Krasii, and P. P.  Mota ).- 6. Shepp and Shiryaev: The Russian Option (P. A. Ernst).- 7. On PioneeringWorks of Albert Shiryaev on Markov Decision Processes and Some Later Developments (E. A. Feinberg).- 8. Model-free analysis of the volatility smile (M. Fukasawa).- 9. A New Look at Optional Semimartingales (L. I. Galtchouk).- 10. On the probabilistic solution of ODEs by MonteCarlo generation of random trees (Q. Huang, and N. Privault).- 11. Skew Brownian Motion and Related Diffusions (I. Karatzas).- 12. Self-Consistent Transport in Heterogeneous-Agent Models (A. Lyasoff).- 13. Martingale functions of a Brownian Motion and their relation with general solutions of functional equations (M. Mania, and R. Tevzadze).- 14. Pricing under the Benchmark Approach (E. Platen).- 15. The Nonlinear Volterra Integral Equation for the Early Exercise Boundary of American Put Option (M. Shashiashvili, B. Dochviri, and G. Lominashvili).- 16. Brownian Motion and the Fredholm Determinant (K. Tanaka).- 17. F-divergences and predictable processes in Probability and Mathematical Finance (L. Vostrikova).- 18. Shareholder Unanimity: A Survey from the Viewpoint of Incomplete Markets (M. Zierhut, and C. Hara).- 19 Hierarchical Structure of Uncertainty (T. Adachi).-Part II. Probability Theory and Statistics of Random Processes.- 20. Spectral characterization of the family of $\alpha$-Stable processes that generalize Gaussian process models (N. Azzaoui, G. Peters, A. Guillin, and T. Matsui).- 21.Stationary Processes, Wiener-Granger Causality, and Matrix Spectral Factorization. (L. Ephremidze, and S. Vatsadze).- 22. On Markovian sufficient statistics in non-additive disorder problems for jump-diffusion processes (P. V. Gapeev).- 23. Maximum Likelihood Estimators for Diffusion–type Processes (N. Kordzakhia, A. Novikov, A. Shiryaev, and S. Alexander).- 24. On Dobrushin’s Central Limit Theorem for non-homogeneous Markov chains   (A. Nurieva, and A. Veretennikov).- 25. Limit Theorems on the Sojourn Time of a Stochastic Walk at a Multidimensional Lattice Point (G. Popov, and E. Yarovaya).- 26. Symmetric Case of Locks, Bombs and Testing Model (I. M. Sonin) .- 27. Normal Distribution: Some Recent Results and Twelve Open Questions (J. M. Stoyanov).

Über Autor(innen)

Pavel Chigansky obtained his PhD degree in Electrical Engineering from Tel Aviv University under the supervision of Prof. Robert Liptser.  He  is currently a professor at the Department of Statistics and Data Science of the Hebrew University of Jerusalem. His research interests include Stochastic Analysis, Nonlinear Filtering, and Mathematical Statistics.

Nino Kordzakhia graduated from Tbilisi State University with Master's degree (with merit) in Mathematics. Then she completed her postgraduate study at Steklov Mathematical Institute (Moscow) with PhD degree under the supervision of Professor Albert Shiryaev. Currently, Nino is an academic at Macquarie University (Australia). Her research interests include Statistics of Stochastic Processes, Pricing of Financial Derivatives, Risk Management of Energy Markets, and Data Driven Uncertainty Quantification Models.