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
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;
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. ;
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
2021
4.
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;
2020
5.
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, “The joint law of a max-continuous local submartingale and its maximum”, Theory Probab. Appl., 65:4 (2021), 545–557
2019
8.
A. A. Gushchin, M. A. Urusov, “Minimal embeddings of integrable processes in a Brownian motion”, Russian Math. Surveys, 74:5 (2019), 953–955
2020
9.
A. A. Gushchin, S. S. Leshchenko, “Testing hypotheses for measures with different masses: Four optimization problems”, Theory Probab. Math. Stat., 101 (2020), 109–117
2018
10.
Alexander Gushchin, Nino Kordzakhia, Alexander Novikov, “Translation invariant statistical experiments with independent increments”, Stat. Inference Stoch. Process., 21:2 (2018), 363–383
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
12.
A. A. Gushchin, “The joint law of terminal values of a nonnegative submartingale and its compensator”, Theory Probab. Appl., 62:2 (2018), 216–235
2017
13.
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, M. A. Urusov, “Processes that can be embedded in a geometric Brownian motion”, Theory Probab. Appl., 60:2 (2016), 246–262
2014
19.
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, “On pathwise counterparts of Doob's maximal inequalities”, Proc. Steklov Inst. Math., 287:1 (2014), 118–121
21.
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
22.
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.
2013
23.
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
24.
A. A. Gushchin, “A characterization of a minimax test in the problem of testing two composite hypotheses”, Dokl. Math., 87:3 (2013), 345–347
25.
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
26.
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
2012
27.
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
2011
28.
A. A. Gushchin, U. Küchler, “On estimation of delay location”, Stat. Inference Stoch. Process., 14:3 (2011), 273–305
A. A. Gushchin, “Utility maximization in some markets admitting arbitrage”, Theory Probab. Appl., 55:3 (2011), 548
30.
A. A. Gushchin, “Dual characterization of the value function in the robust utility maximization problem”, Theory Probab. Appl., 55:4 (2011), 611–630
31.
Yu. S. Mishura, A. A. Gushchin, “International Conference “Modern Stochastics: Theory and Applications II””, Theory Probab. Appl., 55:4 (2011), 732
2009
32.
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
33.
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
2008
34.
A. A. Gushchin, “On an extension of the notion of $f$-divergence”, Theory Probab. Appl., 52:3 (2008), 439–455
2006
35.
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 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
2005
37.
A. A. Gushchin, Measures of informativity and their applications in statistics and finance, Minicourse at Helsinki University of Technology, May 3–9, 2005, 2005
38.
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
2004
39.
A. A. Gushchin, U. Küchler, “On oscillations of the geometric Brownian motion with time-delayed drift”, Statist. Probab. Lett., 70:1 (2004), 19–24
A. A. Gushchin, U. Küchler, “On recovery of a measure from its symmetrization”, Theory Probab. Appl., 49:2 (2005), 323–333
2003
41.
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 parametric statistical models for stationary solutions of affine stochastic delay differential equations”, Math. Methods Statist., 12:1 (2003), 31–61
43.
A. A. Gushchin, “On Fano's lemma and similar inequalities for the minimax risk”, Theory Probab. Math. Statist., 2003, no. 67, 29–41
2002
44.
A. A. Gushchin, É. Mordecki, “Bounds on Option Prices for Semimartingale Market Models”, Proc. Steklov Inst. Math., 237 (2002), 73–113
2001
45.
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
46.
A. A. Gushchin, E. Valkeila, “Exponential statistical experiments: their properties and convergence results”, Statist. Decisions, 19:2 (2001), 173–190
47.
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
48.
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
49.
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
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. 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
1999
52.
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, “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
1998
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
1997
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.
1996
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
1995
61.
A. A. Gushchin, “On asymptotic optimality of estimators of parameters under the LAQ condition”, Theory Probab. Appl., 40:2 (1995), 261–272
62.
A. A. Gushchin, On efficiency bounds for estimating the offspring mean in a branching process, WIAS Preprint No. 175, WIAS, Berlin, 1995 , 25 pp.
63.
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
64.
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
65.
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
1994
66.
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
67.
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
68.
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
69.
A. A. Gushchin, “On the convergence of sequences of semimartingales and their components”, Proc. Steklov Inst. Math., 202 (1994), 35–95
1992
70.
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
1993
71.
A. A. Gushchin, “A Regular Filtered Statistical Model and Families of Martingales”, Theory Probab. Appl., 37:1 (1993), 43–46
1992
72.
A. A. Gushchin, “On quasi-score processes”, Ann. Acad. Sci. Fenn. Ser. A I Math., 17:1 (1992), 29–38
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
1990
74.
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
75.
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
76.
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
1991
77.
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
78.
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
1989
79.
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
80.
A. A. Gushchin, “Rao-Cramér inequalities on a space with filtration”, Russian Math. Surveys, 44:4 (1989), 205–206
81.
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
82.
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
83.
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
1988
84.
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
1987
85.
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
86.
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
1985
87.
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
1983
88.
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.
89.
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.
1982
90.
A. A. Gushchin, “Weakly predictable random fields”, Soviet Math. Dokl., 26:3 (1982), 725–727
91.
A. A. Gushchin, “On the general theory of random fields on the plane”, Russian Math. Surveys, 37:6 (1982), 55–80
1983
92.
A. A. Gushchin, “On absolute continuity and singularity of the distributions of random fields”, Math. USSR-Sb., 46:2 (1983), 161–170
1981
93.
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
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