01.01.05 (Probability theory and mathematical statistics)
Birth date:
18.09.1958
E-mail:
Keywords:
stochastic analysis,
theory of martingales,
Hellinger processes,
statistics of stochastic processes,
parameter estimation,
mathematical finance.
Main publications:
A. A. Gushchin, É. Mordecki, “Bounds on Option Prices for Semimartingale Market Models”, Proc. Steklov Inst. Math., 237 (2002), 73–113
A. A. Gushchin, U. Küchler, “On stationary solutions of delay differential equations driven by a Lévy process”, Stochastic Process. Appl., 88:2 (2000), 195–211
A. A. Gushchin, U. Küchler, “Asymptotic inference for a linear stochastic differential equation with time delay”, Bernoulli, 5:6 (1999), 1059–1098
A. A. Gushchin, “On asymptotic optimality of estimators of parameters under the LAQ condition”, Theory Probab. Appl., 40:2 (1995), 261–272
A. A. Gushchin, “On the general theory of random fields on the plane”, Russian Math. Surveys, 37:6 (1982), 55–80
A. A. Gushchin, U. Küchler, “On stationary solutions of delay differential equations driven by a Lévy process”, Stochastic Process. Appl., 88:2 (2000), 195–211
Alexander Gushchin, Mikhail Urusov, Mihail Zervos, “On the submartingale/supermartingale property of diffusions in natural scale”, Proc. Steklov Inst. Math., 287:1 (2014), 122–132
10.
A. A. Gushchin, U. Küchler, “On estimation of delay location”, Stat. Inference Stoch. Process., 14:3 (2011), 273–305
A. A. Gushchin, “Dual characterization of the value function in the robust utility maximization problem”, Theory Probab. Appl., 55:4 (2011), 611–630
12.
A. A. Gushchin, E. Valkeila, “Approximations and limit theorems for likelihood ratio processes in the binary case”, Statist. Decisions, 21:3 (2003), 219–260
A. A. Gushchin, U. Küchler, “On recovery of a measure from its symmetrization”, Theory Probab. Appl., 49:2 (2005), 323–333
17.
Dmitriy Borzykh, Alexander Gushchin, “On the denseness of the subset of discrete distributions in a certain set of two-dimensional distributions”, Mod. Stoch., Theory Appl., 9:3 (2022), 265–277;
Alexander Gushchin, Ilya Pavlyukevich, Marian Ritsch, “Drift estimation for a L\evy–driven Ornstein–Uhlenbeck process with heavy tails”, Stat. Inference Stoch. Process., 23:3 (2020), 553–570
A. A. Gushchin, R. V. Khasanov, I. S. Morozov, “Some functional analytic tools for utility maximization”, Modern stochastics and applications, Springer Optimization and Its Applications, 90, eds. V. Korolyuk, N. Limnios, Y. Mishura, L. Sakhno, G. Shevchenko, Springer, 2014, 267–285
A. A. Gushchin, “A characterization of a minimax test in the problem of testing two composite hypotheses”, Dokl. Math., 87:3 (2013), 345–347
24.
Yuri Yakubovich, Oleg Rusakov, Alexander Gushchin, “Functional limit theorem for the sums of PSI-processes with random intensities”, Mathematics, 10:21 (2022), 3955 , 17 pp. ;
A. A. Gushchin, “On possible relations between an increasing process and its compensator in the non-integrable case”, Russian Math. Surveys, 73:5 (2018), 928–930
27.
Alexander Gushchin and Esko Valkeila, “Quadratic Approximation for Log-Likelihood Ratio Processes”, Modern Problems of Stochastic Analysis and Statistics, Selected Contributions in Honor of Valentin Konakov, Springer Proceedings in Mathematics & Statistics, 208, eds. Vladimir Panov, Springer International Publishing AG, Cham, 2017, 179–215
A. A. Gushchin, “On pathwise counterparts of Doob's maximal inequalities”, Proc. Steklov Inst. Math., 287:1 (2014), 118–121
30.
A. A. Gushchin, “Utility maximization in some markets admitting arbitrage”, Theory Probab. Appl., 55:3 (2011), 548
31.
A. A. Gushchin, D. A. Zhdanov, “A minimax result for $f$-divergences”, From stochastic calculus to mathematical finance, The Shiryaev Festschrift, eds. Yu. Kabanov, R. Liptser and J. Stoyanov, Springer, Berlin, 2006, 287–294
A. A. Gushchin, “On absolute continuity and singularity of the distributions of random fields”, Math. USSR-Sb., 46:2 (1983), 161–170
34.
Guschin A. A., Nedoshivin M. A., “O konstruktsii Perkinsa v zadache vlozheniya Skorokhoda”, Tezisy dokladov, predstavlennykh na Sedmoi mezhdunarodnoi konferentsii po stokhasticheskim metodam. I. (pos. Divnomorskoe, Gelendzhik, 02–09 iyunya 2022 g.), Teoriya veroyatn. i ee primen., 67, no. 4, 2022, 831
35.
Alexander A. Gushchin, Assylliya K. Zhunussova, “Single jump filtrations: preservation of the local martingale property with respect to the filtration generated by the local martingale”, Operator Theory and Harmonic Analysis, OTHA 2020, Springer Proc. Math. Statist., 358, Springer, Cham, 2021, 219–231;
36.
A. A. Gushchin, S. S. Leshchenko, “Testing hypotheses for measures with different masses: Four optimization problems”, Theory Probab. Math. Stat., 101 (2020), 109–117
A. A. Gushchin, “On the upper hedging price of nonnegative contingent claims”, Modern problems of mathematics and mechanics. Volume VIII. Mathematics. Issue 3. To the 80th anniversary of Mechanics and Mathematics Department of MSU, eds. A. N. Shiryaev, A. V. Lebedev, MSU Press, Moscow, 2013, 60–72
39.
A. A. Gushchin, “On a connection between superhedging prices and the dual problem in utility maximization”, Advanced finance and stochastics, Book of Abstracts (Moscow, 24–28 June 2013), eds. M. Zhitlukhin and A. Muravlev, Steklov Mathematical Institute, Moscow, 2013, 60–61
40.
A. Gushchin, “Translation invariant statistical experiments with independent increments”, Russian-Chinese Seminar on Asymptotic Methods in Probability Theory and Mathematical Statistics. Programme and Abstracts (St.Petersburg, 10–14 June, 2013), The Euler International Mathematical Institute, 2013, 24 http://www.pdmi.ras.ru/EIMI/2013/RChS/prog.pdf
41.
A. A. Gushchin, “On a structure of a minimax test in testing composite hypotheses”, International conference “Stochastic Optimization and Optimal Stopping”. Book of abstracts (Moscow, 24–28 September 2012), eds. Mikhail Zhitlukhin and Alexey Muravlev, Steklov Mathematical Institute, Moscow, 2012, 79–80
42.
A. A. Guschin, “O maksimizatsii robastnoi poleznosti so shtrafnoi funktsiei”, XVI Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam (Sankt-Peterburg, 19–24 maya 2009 g.), Obozrenie prikladnoi i promyshlennoi matematiki, 16, no. 2, 2009, 260–261
43.
A. A. Guschin, “Odna lemma iz teorii prostranstv Orlicha”, X Vserossiiskii simpozium po prikladnoi i promyshlennoi matematike (Sochi, 1–8 oktyabrya 2009 g.), Obozrenie prikladnoi i promyshlennoi matematiki, 16, no. 6, 2009, 1056–1057
44.
A. A. Gushchin, “On robust utility maximization”, International Conference “Modern Stochastics: Theory and Applications” (Kyiv, June 19–23, 2008), Conference Materials, Kyiv National Taras Shevchenko University, 2006, 134–135
45.
A. A. Gushchin, Measures of informativity and their applications in statistics and finance, Minicourse at Helsinki University of Technology, May 3–9, 2005, 2005
46.
A. A. Guschin, “$f$-divergentsiya konechno-additivnykh mer”, XII Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam (Sochi, 1–7 oktyabrya 2005 g.), Obozrenie prikladnoi i promyshlennoi matematiki, 12, no. 3, 2005, 657–658
47.
A. A. Gushchin, U. Küchler, “On parametric statistical models for stationary solutions of affine stochastic delay differential equations”, Math. Methods Statist., 12:1 (2003), 31–61
48.
A. A. Gushchin, “On Fano's lemma and similar inequalities for the minimax risk”, Theory Probab. Math. Statist., 2003, no. 67, 29–41
49.
A. A. Gushchin, E. Valkeila, “Exponential approximation of statistical experiments”, Asymptotic methods in probability and statistics with applications (St. Petersburg, 1998), Stat. Ind. Technol., eds. N. Balakrishnan, I. A. Ibragimov, V. B. Nevzorov, Birkhäuser Boston, Boston, MA, 2001, 409–423
50.
A. A. Gushchin, E. Valkeila, “Exponential statistical experiments: their properties and convergence results”, Statist. Decisions, 19:2 (2001), 173–190
51.
A. A. Guschin, O. V. Lepskii, “Ob asimptoticheskom povedenii otsenok parametrov”, VIII Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam (Ioshkar-Ola, 1–6 dekabrya 2001 g.), Obozrenie prikladnoi i promyshlennoi matematiki, 8, no. 2, 2001, 755–756
52.
A. A. Gushchin, E. Valkeila, “Approximations for likelihood ratio processes”, VIII Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam (Ioshkar-Ola, 1–6 dekabrya 2001 g.), Obozrenie prikladnoi i promyshlennoi matematiki, 8, no. 2, 2001, 819–821
53.
A. A. Guschin, U. Kyukhler, “Ob otsenivanii parametra v odnoi modeli statsionarnykh gaussovskikh nablyudenii”, VII Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam (Sochi, 1–6 oktyabrya 2000 g.), Obozrenie prikladnoi i promyshlennoi matematiki, 7, no. 2, 2000, 489–490
54.
A. A. Gushchin, E. Valkeila, “On convergence to exponential-type statistical models”, Abstracts of communications, International conference “Asymptotic Methods in Probability and Mathematical Statistics” dedicated to the 50th Anniversary of the Chair of Probability and Statistics in St. Petersburg University (St. Petersburg, June 24–28, 1998), St. Petersburg University, 1998, 107–112
55.
A. A. Guschin, U. Kyukhler, “O suschestvovanii statsionarnogo resheniya stokhasticheskogo differentsialnogo uravneniya s zapazdyvaniem, upravlyaemogo protsessom Levi”, V Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam (Ioshkar-Ola, 6–12 dekabrya 1998 g.), Obozrenie prikladnoi i promyshlennoi matematiki, 5, no. 2, 1998, 217–218
56.
A. A. Guschin, Issledovaniya po teorii semimartingalov i ikh statistike, Diss. … doktora fiz.-matem. nauk, Matematicheskii institut im. V. A. Steklova, Moskva, 1997 , 223 pp.
57.
A. A. Guschin, Issledovaniya po teorii semimartingalov i ikh statistike, Avtoreferat diss. … doktora fiz.-matem. nauk, Matematicheskii institut im. V. A. Steklova, Moskva, 1997 , 26 pp.
58.
A. A. Gushchin, “On taking limits under the compensator sign”, Probability theory and mathematical statistics, Proceedings of the Euler Institute seminars dedicated to the memory of Kolmogorov (St. Petersburg, 1993), eds. I. A. Ibragimov and A. Yu. Zaitsev, Gordon and Breach, Amsterdam, 1996, 185–192
59.
A. A. Gushchin, “On an information-type inequality for the Hellinger process”, Probability theory and mathematical statistics, Proceedings of the Seventh Japan–Russia Symposium (Tokyo, 1995), eds. S. Watanabe, M. Fukushima, Yu. V. Prohorov, A. N. Shiryaev, World Scientific, Singapore, 1996, 83–109
60.
A. A. Gushchin, “On some inequalities of Cramér–Rao type”, Uspekhi teorii veroyatnostei ee primenenii II (Moskva, 3–8 oktyabrya 1993 g.), Trudy chetvertogo rossiisko–finskogo simpoziuma po teorii veroyatnostei i matematicheskoi statistike, eds. A. N. Shiryaev, A. V. Melnikov, Kh. Niemi, E. Valkeila, TVP, Moskva, 1996, 59–66
61.
A. A. Gushchin, On efficiency bounds for estimating the offspring mean in a branching process, WIAS Preprint No. 175, WIAS, Berlin, 1995 , 25 pp.
62.
A. A. Gushchin, “On semiparametric estimation for functionals of stochastic processes”, 21st European Meeting of Statisticians. Programme & Abstracts (Aarhus, August 21–25, 1995), University of Aarhus, 1995, 78
63.
A. A. Gushchin, “A lower bound for the variation distance between distributions of stochastic processes”, Abstract. Japan–Russia Symposium on Probability Theory and Mathematical Statistics (Tokyo, July 26–30, 1995), The Meiji Mutual Life Insurance Co. Corporate Training Center, 1995, 75
64.
A. A. Guschin, U. Kyukhler, “Otsenivanie parametrov po nablyudeniyu za resheniem lineinogo stokhasticheskogo differentsialnogo uravneniya s zapazdyvaniem”, Vtoraya Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam (Ioshkar-Ola, 18–23 dekabrya 1995 g.), Tezisy dokladov, TVP, Moskva, 1995, 44–45
65.
A. A. Gushchin, “On the asymptotic optimality of estimates of parameters for locally asymptotically quadratic statistical experiments”, Russian Math. Surveys, 49:2 (1994), 159–160
66.
A. A. Guschin, “Ob asimptoticheskoi effektivnosti otsenok funktsionalov ot sluchainykh protsessov”, Vserossiiskaya shkola-kollokvium po stokhasticheskim metodam geometrii i analiza. Tezisy dokladov (Abrau–Dyurso, 25 sentyabrya–2 oktyabrya 1994 g.), TVP, Moskva, 1994, 33–34
67.
A. A. Gushchin, “Efficiency bounds for estimating the offspring mean in a branching process”, Proceedings of the Workshop on Stochastics and Finance (Berlin, September 5–10, 1994), Humboldt University, Berlin, 1994, 32–33
68.
A. A. Gushchin, “On the convergence of sequences of semimartingales and their components”, Proc. Steklov Inst. Math., 202 (1994), 35–95
69.
A. A. Gushchin, “On convergence of a sequence of compensators of increasing processes”, Probability theory and mathematical statistics (Kiev, 1991), eds. A. N. Shiryaev et al., World Scientific, Singapore, 1992, 111–124
70.
A. A. Gushchin, “A Regular Filtered Statistical Model and Families of Martingales”, Theory Probab. Appl., 37:1 (1993), 43–46
71.
A. A. Gushchin, Yu. S. Mishura, “The Davis inequalities and the Gundy decomposition for two-parameter strong martingales. III”, Theory Probab. Math. Statist., 1992, no. 44, 45–51
72.
Yu. S. Mishura, A. A. Gushchin, “Two-parameter strong martingales: inequalities for quadratic variation and some decompositions”, Probability theory and mathematical statistics (Vilnius, 1989), Vol. II, eds. B. Grigelionis et al., VSP / Mokslas, Utrecht / Vilnius, 1990, 181–192 https://www.degruyter.com/document/doi/10.1515/9783112319024/html
73.
A. A. Gushchin, “Improvement and generalization of the Cramér-Rao inequality for a filtered space”, Probability theory and mathematical statistics (Vilnius, 1989), Vol. I, eds. B. Grigelionis et al., VSP / Mokslas, Utrecht / Vilnius, 1990, 480–489
74.
A. A. Gushchin, A. I. Ekushov, “Estimation of the expected reward from programmed control for a certain type of controllable Markov sequence”, Theory Probab. Appl., 35:3 (1990), 431–442
75.
A. A. Gushchin, Yu. S. Mishura, “The Davis inequalities and the Gundy decomposition for two-parameter strong martingales. II”, Theory Probab. Math. Statist., 1991, no. 43, 65–76
76.
A. A. Gushchin, Yu. S. Mishura, “The Davis inequalities and the Gundy decomposition for two-parameter strong martingales. I”, Theory Probab. Math. Statist., 1991, no. 42, 29–37
77.
A. A. Gushchin, “A remark on the asymptotic behavior of minimax risk in distinguishing processes of diffusion type”, Statistics and control of random processes (Preila, 1987), Nauka, Moscow, 1989, 48–55
78.
A. A. Gushchin, “Rao-Cramér inequalities on a space with filtration”, Russian Math. Surveys, 44:4 (1989), 205–206
79.
A. A. Gushchin, “Cramér–Rao type inequality for a filtered space”, Fifth International Vilnius Conference on Probability Theory and Mathematical Statistics, Abstracts of Communications (Vilnius, June 26 – July 1, 1989), V. I: A–L, Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR, Vilnius, 1989, 190–191
80.
Yu. S. Mishura, A. A. Guschin, “Razlozheniya silnykh martingalov i semimartingalov, zadannykh na ploskosti”, Pyataya mezhdunarodnaya Vilnyusskaya konferentsiya po teorii veroyatnostei i matematicheskoi statistike, Tezisy dokladov (Vilnyus, 26 iyunya – 1 iyulya 1989 g.), T. IV: M–Ya, Institut matematiki i kibernetiki Litovskoi SSR, Vilnyus, 1989, 57–58
81.
A. A. Gushchin, “Cramér–Rao type inequality for filtered statistical experiments”, XXXIII Semester on Robustness and Nonparametric Statistics, Abstracts of Lectures (Warsaw, March 1 – May 31, 1989), Part I, Stefan Banach International Mathematical Center, Warsaw, 1989, 66–67
82.
A. A. Gushchin, “Stochastic integration with respect to strong martingales in the plane”, Lectures in mathematics and its applications, Vol. 2, No. 2, Ross. Akad. Nauk, Inst. Mat. im. Steklova, Moscow, 1988, 242–256
83.
A. A. Guschin, “Ob “ostanovke” silnykh martingalov na ploskosti”, XXI shkola-kollokvium po teorii veroyatnostei i matematicheskoi statistike, Tezisy dokladov (Bakuriani, 21 fevralya – 1 marta 1987 g.), Metsniereba, Tbilisi, 1987, 12
84.
A. A. Gushchin, “On asymptotic behaviour of minimax risk in the problem of testing two simple hypotheses”, 5th European Young Statisticians Meeting (Aarhus, August 17–21, 1987), eds. J. L. Jensen, M. Sørensen, Aarhus University, Aarhus, 1987, 60–62
85.
A. A. Guschin, E. I. Kolomiets, “Nekotorye neravenstva dlya veroyatnostei oshibok razlicheniya dvukh prostykh gipotez”, Chetvertaya mezhdunarodnaya Vilnyusskaya konferentsiya po teorii veroyatnostei i matematicheskoi statistike, Tezisy dokladov (Vilnyus, 24–29 iyunya 1985 g.), T. 1: A-I, Institut matematiki i kibernetiki AN Litovskoi SSR, Vilnyus, 1985, 198–199
86.
A. A. Guschin, K obschei teorii sluchainykh polei (martingalnyi podkhod), Diss. … kand. fiz.-matem. nauk, Matematicheskii institut im. V. A. Steklova, Moskva, 1983 , 108 pp.
87.
A. A. Guschin, K obschei teorii sluchainykh polei (martingalnyi podkhod), Avtoreferat diss. … kand. fiz.-matem. nauk, Matematicheskii institut im. V. A. Steklova, Moskva, 1983 , 12 pp.
88.
A. A. Gushchin, “Weakly predictable random fields”, Soviet Math. Dokl., 26:3 (1982), 725–727
89.
A. A. Guschin, “Ob absolyutnoi nepreryvnosti i singulyarnosti raspredelenii sluchainykh polei”, Tretya Vilnyusskaya konferentsiya po teorii veroyatnostei i matematicheskoi statistike, Tezisy dokladov (Vilnyus, 22–27 iyunya 1981 g.), T. 1 (A–K), Institut matematiki i kibernetiki AN Litovskoi SSR, Vilnyus, 1981, 159–160
90.
A. A. Gushchin, U. Küchler, “Addendum to: “Asymptotic inference for a linear stochastic differential equation with time delay” [Bernoulli 5 (1999), no. 6, 1059–1098]”, Bernoulli, 7:4 (2001), 629–632
Yu. S. Mishura, A. A. Gushchin, “International Conference “Modern Stochastics: Theory and Applications II””, Theory Probab. Appl., 55:4 (2011), 732
92.
A. A. Gushchin, “Book review: Christopher C. Heyde. “Quasi-Likelihood and Its Application. A General Approach to Optimal Parameter Estimation””, Theory Probab. Appl., 44:1 (2000), 222–224
93.
Stokhasticheskoe ischislenie, martingaly i ikh primeneniya, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Alberta Nikolaevicha Shiryaeva, Trudy MIAN, 287, ed. A. A. Guschin, A. G. Sergeev, MAIK «Nauka/Interperiodika», M., 2014 , 319 pp.
Martingales with respect to special filtration Alexander Gushchin International Conference "Theory of Probability and Its Applications: P. L. Chebyshev – 200" (The 6th International Conference on Stochastic Methods) May 20, 2021 18:00
О задаче максимизации робастной полезности A. A. Gushchin Seminar of the Department of Probability Theory "Stochastic Analysis: Theory and Applications", Steklov Mathematical Institute of RAS December 7, 2006
21.
О задаче максимизации полезности A. A. Gushchin Principle Seminar of the Department of Probability Theory, Moscow State University November 2, 2005
Books in Math-Net.Ru
Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 287, ed. A. A. Gushchin, A. G. Sergeev, 2014, 319 с. http://mi.mathnet.ru/book1573