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Teoriya Veroyatnostei i ee Primeneniya, 1962, Volume 7, Issue 3, Pages 336–342 (Mi tvp4730)  

This article is cited in 26 scientific papers (total in 26 papers)

Short Communications

Ein beispiel der uneindeutlichkeit der Lösung der stochastischen integralgleichung von K. Ito

I. V. Girsanov

Moscow
Abstract: In dieser Artikel beweißt man, daß die stochastische Integralgleichung
κj(ω)=κs(ω)+ts|κk(ω)|αdξu(ω)κj(ω)=κs(ω)+ts|κk(ω)|αdξu(ω)
bei 0<α<120<α<12 viele Lösungen hat.
Received: 01.09.1960
English version:
Theory of Probability and its Applications, 1962, Volume 7, Issue 3, Pages 325–331
DOI: https://doi.org/10.1137/1107031
Document Type: Article
Language: Russian
Citation: I. V. Girsanov, “Ein beispiel der uneindeutlichkeit der Lösung der stochastischen integralgleichung von K. Ito”, Teor. Veroyatnost. i Primenen., 7:3 (1962), 336–342; Theory Probab. Appl., 7:3 (1962), 325–331
Citation in format AMSBIB
\Bibitem{Gir62}
\by I.~V.~Girsanov
\paper Ein beispiel der uneindeutlichkeit der L\"osung der stochastischen integralgleichung von K.~Ito
\jour Teor. Veroyatnost. i Primenen.
\yr 1962
\vol 7
\issue 3
\pages 336--342
\mathnet{http://mi.mathnet.ru/tvp4730}
\transl
\jour Theory Probab. Appl.
\yr 1962
\vol 7
\issue 3
\pages 325--331
\crossref{https://doi.org/10.1137/1107031}
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  • https://www.mathnet.ru/eng/tvp4730
  • https://www.mathnet.ru/eng/tvp/v7/i3/p336
  • This publication is cited in the following 26 articles:
    1. Ilya Pavlyukevich, Georgiy Shevchenko, “Stochastic selection problem for a Stratonovich SDE with power non-linearity”, Bernoulli, 31:2 (2025)  crossref
    2. Alexander Schnurr, Sebastian Rickelhoff, “From Markov processes to semimartingales”, Probab. Surveys, 20:none (2023)  crossref
    3. Dai Taguchi, “On the strong convergence rate for the Euler–Maruyama scheme of one-dimensional SDEs with irregular diffusion coefficient and local time”, Journal of Complexity, 74 (2023), 101695  crossref
    4. Yanling Zhu, Kai Wang, Yong Ren, “Dynamics of a mean-reverting stochastic volatility equation with regime switching”, Communications in Nonlinear Science and Numerical Simulation, 83 (2020), 105110  crossref
    5. Ilya Pavlyukevich, Georgiy Shevchenko, “Stratonovich stochastic differential equation with irregular coefficients: Girsanov's example revisited”, Bernoulli, 26:2 (2020)  crossref
    6. Dai Taguchi, Akihiro Tanaka, Lecture Notes in Mathematics, 2252, Séminaire de Probabilités L, 2019, 165  crossref
    7. Hiroya Hashimoto, Takahiro Tsuchiya, “Stability problems for Cantor stochastic differential equations”, Stochastic Processes and their Applications, 128:1 (2018), 211  crossref
    8. Kouji Yano, Marc Yor, “Around Tsirelson's equation, or: The evolution process may not explain everything”, Probab. Surveys, 12:none (2015)  crossref
    9. Henri Schurz, Springer Proceedings in Mathematics, 7, Stochastic Differential Equations and Processes, 2012, 1  crossref
    10. Yongku Kim, Suk Bok Kang, L. Mark Berliner, “Bayesian diffusion process models with time-varying parameters”, Journal of the Korean Statistical Society, 41:1 (2012), 137  crossref
    11. Marco Romito, Progress in Probability, 63, Seminar on Stochastic Analysis, Random Fields and Applications VI, 2011, 227  crossref
    12. Ioannis Karatzas, Albert Shiryaev, Mykhaylo Shkolnikov, “On the one-sided Tanaka equation with drift”, Electron. Commun. Probab., 16:none (2011)  crossref
    13. A.S. Cherny, “On the strong and weak solutions of stochastic differential equations governing Bessel processes”, Stochastics and Stochastic Reports, 70:3-4 (2000), 213  crossref
    14. S. I. Pisanez, “On the existence of strong solutions of diffusion-type stochastic equations in $\mathbb{R}^m$”, Theory Probab. Appl., 42:1 (1998), 179–184  mathnet  mathnet  crossref  crossref  isi
    15. Kiyosi Itô, Makiko Nisio, Selected Papers, 1987, 365  crossref
    16. Takashi Komatsu, “On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations of jump type”, Proc. Japan Acad. Ser. A Math. Sci., 58:8 (1982)  crossref
    17. Mathematics in Science and Engineering, 150, Random Differential Inequalities, 1980, 202  crossref
    18. Stochastic Integration, 1980, 188  crossref
    19. V. A. Lebedev, “On a condition for uniqueness of a solution of a system of stochastic differential equations”, Theory Probab. Appl., 21:2 (1977), 412–419  mathnet  mathnet  crossref
    20. N. V. Krylov, “On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes”, Math. USSR-Izv., 7:3 (1973), 691–709  mathnet  crossref  mathscinet  zmath
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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