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
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
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
8.
A. A. Gushchin, M. A. Urusov, “Minimal embeddings of integrable processes in a Brownian motion”, Russian Math. Surveys, 74:5 (2019), 953–955
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
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
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
18.
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
20.
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
21.
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
22.
A. A. Gushchin, “A characterization of a minimax test in the problem of testing two composite hypotheses”, Dokl. Math., 87:3 (2013), 345–347
23.
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
25.
A. A. Gushchin, “Dual characterization of the value function in the robust utility maximization problem”, Theory Probab. Appl., 55:4 (2011), 611–630
26.
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
27.
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
28.
A. A. Gushchin, “On an extension of the notion of $f$-divergence”, Theory Probab. Appl., 52:3 (2008), 439–455
29.
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, U. Küchler, “On recovery of a measure from its symmetrization”, Theory Probab. Appl., 49:2 (2005), 323–333
33.
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
35.
A. A. Gushchin, “On Fano's lemma and similar inequalities for the minimax risk”, Theory Probab. Math. Statist., 2003, no. 67, 29–41
36.
A. A. Gushchin, É. Mordecki, “Bounds on Option Prices for Semimartingale Market Models”, Proc. Steklov Inst. Math., 237 (2002), 73–113
37.
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
38.
A. A. Gushchin, E. Valkeila, “Exponential statistical experiments: their properties and convergence results”, Statist. Decisions, 19:2 (2001), 173–190
39.
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
40.
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
41.
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
43.
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, 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
45.
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
46.
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
47.
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
48.
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
49.
A. A. Gushchin, “On asymptotic optimality of estimators of parameters under the LAQ condition”, Theory Probab. Appl., 40:2 (1995), 261–272
50.
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
51.
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
52.
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
53.
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
54.
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
55.
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
56.
A. A. Gushchin, “On the convergence of sequences of semimartingales and their components”, Proc. Steklov Inst. Math., 202 (1994), 35–95
57.
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
58.
A. A. Gushchin, “A Regular Filtered Statistical Model and Families of Martingales”, Theory Probab. Appl., 37:1 (1993), 43–46
59.
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
61.
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
62.
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
63.
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
64.
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
65.
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
66.
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
67.
A. A. Gushchin, “Rao-Cramér inequalities on a space with filtration”, Russian Math. Surveys, 44:4 (1989), 205–206
68.
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
69.
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
70.
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
71.
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
72.
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
73.
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
74.
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
75.
A. A. Gushchin, “Weakly predictable random fields”, Soviet Math. Dokl., 26:3 (1982), 725–727
76.
A. A. Gushchin, “On the general theory of random fields on the plane”, Russian Math. Surveys, 37:6 (1982), 55–80
77.
A. A. Gushchin, “On absolute continuity and singularity of the distributions of random fields”, Math. USSR-Sb., 46:2 (1983), 161–170
78.
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
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.
81.
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.
82.
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.
83.
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.
Proceedings
84.
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
85.
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
86.
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
87.
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
Preprints
88.
A. A. Gushchin, On efficiency bounds for estimating the offspring mean in a branching process, WIAS Preprint No. 175, WIAS, Berlin, 1995 , 25 pp.
Information matherials
89.
Yu. S. Mishura, A. A. Gushchin, “International Conference “Modern Stochastics: Theory and Applications II””, Theory Probab. Appl., 55:4 (2011), 732
Critic, bibliography
90.
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
Miscellaneous
91.
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.
Manuscripts
92.
A. A. Gushchin, Measures of informativity and their applications in statistics and finance, Minicourse at Helsinki University of Technology, May 3–9, 2005, 2005
Letters, errata
93.
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; ; ;
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