Translated by R. Cooke
Preview
Unable to display preview. Download preview PDF.
Bibliography
A.N. Shiryaev. The detection of spontaneous effects. Sov. Math. Dokl., 1961, 2, 740–743.
A.N. Shiryaev. The problem of the most rapid detection of a disturbance in a stationary process. Sov. Math. Dokl., 1961, 2, 795–799.
A.N. Shiryaev. On optimal methods in quickest detection problems. Theory Probab. Appl., 1963, 8(1), 22–46.
A.N. Shiryaev. On the detection of disorder in a manufacturing process, I; II. Theory Probab. Appl., 1963, 8(3), 247–265; 8(4), 402–413.
A.N. Shiryaev. On the theory of decision functions and control of a process of observation based on incomplete information. In: Transactions of the Third Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Liblice,1962). Prague: Czechoslovak Academy of Sciences, 1964, 657–681 (Russian); English translation: Select. Transl. Math. Statist. Probab., 1966, 6, 162–188.
A.N. Shiryaev. Some exact formulas in a ‘disorder’ problem. Theory Probab. Appl., 1965, 10(2), 349–354.
A.N. Shiryaev. Stochastic equations of non-linear filtering by jump-like Markov processes. Problems Inform. Transmiss., 1966, 2(3), 1–18.
A.N. Shiryaev. Some new results in the theory of controlled random processes. In: Transactions of the Fourth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1965). Prague: Czechoslovak Academy of Sciences, 1967, 131–203 (Russian); English translation: Select. Transl. Math. Statist. Probab., 1969, 8, 49–130.
A.N. Shiryaev. Two problems of sequential analysis. Cybernetics, 1967, 3(2), 63–69.
A.N. Shiryaev. Statistical Sequential Analysis: Optimal Stopping Rules. Moscow: Nauka, 1969 (Russian).
R.S. Liptser, A.N. Shiryaev. Statistics of Random Processes, Vol. I, II, 2nd revised and expanded edition. Berlin: Springer, 2001.
R. S. Liptser, A.N. Shiryaev. Theory of Martingales. Dordrecht: Kluwer, 1989 (Math. Appl., Sov. Ser., 49).
J. Jacod, A.N. Shiryaev. Limit Theorems for Stochastic Processes. Berlin: Springer, 1987 (Grundlehren Math. Wiss., 288).
B. I. Grigelionis, A.N. Shiryaev. On Stefan’s problem and optimal stopping rules for Markov processes. Theory Probab. Appl., 1966, 11(4), 541–558.
S.W. Roberts. A comparison of some control chart procedures. Technometrics, 1966, 8, 411–430.
M. Pollak, D. Siegmund. A diffusion process and its applications to detecting a change in the drift of Brownian motion. Biometrika, 1985, 72(2), 267–280.
G. Lorden. Procedures for reacting to a change in a distribution. Ann. Math. Statist., 1971, 42, 1879–1908.
G.V. Moustakides. Optimal stopping times for detecting changes in distributions. Ann. Math. Statist., 1986, 14, 1379–1387.
M. Pollak. Optimal detection of a change in distribution. Ann. Statist., 1985, 13, 206–227.
B. Yakir. A note on optimal detection of a change in distribution. Ann. Statist., 1997, 25, 2117–2126.
B. Yakir, A.M. Krieger, M. Pollak. Detecting a change in regression: first-order optimality. Ann. Statist., 1999, 27, 1896–1913.
A.N. Shiryaev. Minimax optimality of the CUSUM method in the case of continuous time. Uspekhi Mat. Nauk, 1996, 51(4), 173–174 (Russian).
Change-Point Problems (South Hadley, MA, 1992) (eds. E. Carlstein, H.-G. Müller and D. Siegmund). Hayward, CA: Institute of Mathematical Statistics, 1994 (IMS Lecture Notes Monograph Ser., 23).
E. S. Page. Continuous inspection schemes. Biometrika, 1954, 41, 100–115.
E. S. Page. Control charts with warning lines. Biometrika, 1955, 42, 243–257.
D.M. Hawkins, D.H. Olwell. Cumulative Sum Charts and Charting for Quality Improvement. New York: Springer, 1998.
A.N. Shiryaev. Quickest detection problems in the ‘Technical Analysis’ of the financial data. In: Mathematical Finance — Bachelier Congress (Paris, 2000). Berlin: Springer, 2002, 487–521.
R. L. Stratonovich. Conditional Markov processes. Teor. Veroyatn. Primen., 1960, 5(1), 172–195 (Russian).
R. L. Stratonovich. Conditional Markov Processes and their Application to the Theory of Optimal Control. New York: Elsevier, 1968.
E.B. Dynkin. The optimum choice of the instance for stopping a Markov process. Sov. Math. Dokl., 1963, 4, 627–629.
E.B. Dynkin, A.A. Yushkevich. Markov Processes: Theorems and Problems. New York: Plenum Press, 1969.
Y.S. Chow, H. Robbins, D. Siegmund. Great Expectations: The Theory of Optimal Stopping. New York: Houghton Mifflin, 1971.
J. Jacod. Calcul stochastique et problèmes de martingales. Berlin: Springer, 1979 (Lecture Notes in Math., 714).
N.V. Krylov. Controlled Processes of Diffusion Type. Moscow: Nauka, 1977 (Russian).
P.A. Meyer. A short presentation of stochastic calculus. Appendix to: M. Émery. Stochastic Calculus in Manifolds. Berlin: Springer, 1989.
A.N. Shiryaev. Essentials of Stochastic Finance. Facts, Models, Theory. River Edge, NJ: World Scientific, 1999; 2nd corrected Russian edition: Fundamentals of Stochastic Mathematics of Finance, Vol. I: Facts, Models; Vol. II: Theory. Moscow: PHASIS, 2004.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shiryaev, A.N. (2006). From “Disorder” to Nonlinear Filtering and Martingale Theory. In: Bolibruch, †.A.A., et al. Mathematical Events of the Twentieth Century. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-29462-7_18
Download citation
DOI: https://doi.org/10.1007/3-540-29462-7_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23235-3
Online ISBN: 978-3-540-29462-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)