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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 4, Pages 635–654 (Mi tvp751)  

This article is cited in 34 scientific papers (total in 34 papers)

Boundary problems for random walks and large deviations in functional spaces

A. A. Borovkov


Abstract: Asymptotic properties (in the region of large deviations) of the logarithmic probability that the sample paths of a random walk generated by sums of independent addends or by a Poisson process belong to a given open set in $C(0,1)$ or $D(0,1)$ are under consideration.

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English version:
Theory of Probability and its Applications, 1967, 12:4, 575–595

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Received: 11.06.1966

Citation: A. A. Borovkov, “Boundary problems for random walks and large deviations in functional spaces”, Teor. Veroyatnost. i Primenen., 12:4 (1967), 635–654; Theory Probab. Appl., 12:4 (1967), 575–595

Citation in format AMSBIB
\by A.~A.~Borovkov
\paper Boundary problems for random walks and large deviations in functional spaces
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 4
\pages 635--654
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 4
\pages 575--595

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Novikov, “On estimates and the asymptotic behavior of the probability of nonintersection of moving boundaries by sums of independent random variables”, Math. USSR-Izv., 17:1 (1981), 129–145  mathnet  crossref  mathscinet  zmath  isi
    2. A. A. Borovkov, “Boundary-value problems, the invariance principle, and large deviations”, Russian Math. Surveys, 38:4 (1983), 259–290  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. P. Maslov, “Non-standard characteristics in asymptotic problems”, Russian Math. Surveys, 38:6 (1983), 1–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. S. Yu. Dobrokhotov, V. N. Kolokoltsov, V. P. Maslov, “Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation $hu_t=h^2\Delta u/2-V(x)u$”, Theoret. and Math. Phys., 87:3 (1991), 561–599  mathnet  crossref  mathscinet  zmath  isi
    5. S. Yu. Dobrokhotov, V. N. Kolokoltsov, V. Martines Olive, “Asymptotically stable invariant tori of a vector field $V(x)$ and the quasimodes of the operator $V(x)\cdot\nabla-\varepsilon\Delta$”, Math. Notes, 58:2 (1995), 880–884  mathnet  crossref  mathscinet  zmath  isi
    6. R. L. Dobrushin, E. A. Pechersky, “Large Deviations for Random Processes with Independent Increments on Infinite Intervals”, Problems Inform. Transmission, 34:4 (1998), 354–382  mathnet  mathscinet  zmath
    7. A. A. Borovkov, A. A. Mogul'skii, “Large deviations for Markov chains in the positive quadrant”, Russian Math. Surveys, 56:5 (2001), 803–916  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. R. Fatalov, “Point Asymptotics for Probabilities of Large Deviations of the $\omega^2$ Statistics in Verification of the Symmetry Hypothesis”, Problems Inform. Transmission, 40:3 (2004), 212–225  mathnet  crossref  mathscinet  zmath
    9. A. A. Borovkov, K. A. Borovkov, “On probabilities of large deviations for random walks. II. Regular exponentially decaying distributions”, Theory Probab. Appl., 49:3 (2005), 189–206  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. A. A. Borovkov, A. A. Mogul'skii, “On large and superlarge deviations for sums of independent random vectors under the Cramer condition. I”, Theory Probab. Appl., 51:2 (2007), 227–255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. N. S. Arkashov, I. S. Borisov, A. A. Mogul'skii, “Large deviation principle for partial sum processes of moving averages”, Theory Probab. Appl., 52:2 (2008), 181–208  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. A. A. Borovkov, “Large Sample Change-Point Estimation when Distributions Are Unknown”, Theory Probab. Appl., 53:3 (2009), 402–418  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. A. A. Borovkov, A. A. Mogul'skiǐ, “On large deviation principles in metric spaces”, Siberian Math. J., 51:6 (2010), 989–1003  mathnet  crossref  mathscinet  isi  elib
    14. A. A. Borovkov, A. A. Mogul'skii, “Chebyshev type exponential inequalities for sums of random vectors and random walk trajectories”, Theory Probab. Appl., 56:1 (2012), 21–43  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    15. A. A. Borovkov, A. A. Mogul'skiǐ, “Properties of a functional of trajectories which arises in studying the probabilities of large deviations of random walks”, Siberian Math. J., 52:4 (2011), 612–627  mathnet  crossref  mathscinet  isi
    16. A. A. Borovkov, A. A. Mogul'skii, “On large deviation principles for random walk trajectories. I”, Theory Probab. Appl., 56:4 (2011), 538–561  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    17. Theory Probab. Appl., 57:2 (2013), 347–357  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. A. A. Mogul'skiǐ, “The expansion theorem for the deviation integral”, Siberian Adv. Math., 23:4 (2013), 250–262  mathnet  crossref  mathscinet  elib
    19. A. A. Borovkov, A. A. Mogul'skii, “On large deviation principles for random walk trajectories. II”, Theory Probab. Appl., 57:1 (2013), 1–27  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    20. A. A. Mogul'skiǐ, “On the upper bound in the large deviation principle for sums of random vectors”, Siberian Adv. Math., 24:2 (2014), 140–152  mathnet  crossref  mathscinet  elib
    21. A. A. Borovkov, A. A. Mogul'skiǐ, “Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments”, Siberian Adv. Math., 25:1 (2015), 39–55  mathnet  crossref  mathscinet
    22. A. A. Borovkov, A. A. Mogulskii, “Large deviation principles for random walk trajectories. III”, Theory Probab. Appl., 58:1 (2014), 25–37  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    23. A. A. Borovkov, A. A. Mogul'skii, “Moderately large deviation principles for trajectories of random walks and processes with independent increments”, Theory Probab. Appl., 58:4 (2014), 562–581  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    24. A. A. Borovkov, A. A. Mogul'skiǐ, “Inequalities and principles of large deviations for the trajectories of processes with independent increments”, Siberian Math. J., 54:2 (2013), 217–226  mathnet  crossref  mathscinet  isi
    25. A. A. Borovkov, A. A. Mogul'skiǐ, “Large deviation principles for the finite-dimensional distributions of compound renewal processes”, Siberian Math. J., 56:1 (2015), 28–53  mathnet  crossref  mathscinet  isi  elib  elib
    26. A. A. Borovkov, A. A. Mogul'skii, “Large deviation principles for trajectories of compound renewal processes. I”, Theory Probab. Appl., 60:2 (2016), 207–221  mathnet  crossref  crossref  mathscinet  isi  elib
    27. Klebaner F.C., Logachov A.V., Mogulskii A.A., “Large Deviations For Processes on Half-Line”, Electron. Commun. Probab., 20 (2015), 75, 1–14  crossref  isi
    28. A. A. Mogul'skiǐ, “The large deviation principle for a compound Poisson process”, Siberian Adv. Math., 27:3 (2017), 160–186  mathnet  crossref  crossref  elib
    29. A. A. Mogul'skiǐ, “On a property of the Legendre transform”, Siberian Adv. Math., 28:1 (2018), 65–73  mathnet  crossref  crossref  elib
    30. Djellout H., Guillin A., Samoura Ya., “Estimation of the Realized (Co-)Volatility Vector: Large Deviations Approach”, Stoch. Process. Their Appl., 127:9 (2017), 2926–2960  crossref  isi
    31. A. A. Mogul'skiǐ, “The extended large deviation principle for a process with independent increments”, Siberian Math. J., 58:3 (2017), 515–524  mathnet  crossref  crossref  isi  elib  elib
    32. F. C. Klebaner, A. V. Logachov, A. A. Mogulskii, “Extended large deviation principle for trajectories of processes with independent and stationary increments on the half-line”, Problems Inform. Transmission, 56:1 (2020), 56–72  mathnet  crossref  crossref  isi  elib
    33. A. A. Mogulskii, “Rasshirennyi printsip bolshikh uklonenii dlya traektorii obobschennogo protsessa vosstanovleniya”, Matem. tr., 24:1 (2021), 142–174  mathnet  crossref
    34. A. A. Borovkov, A. V. Logachev, A. A. Mogulskii, “Neravenstva chebyshevskogo tipa i printsipy bolshikh uklonenii”, Teoriya veroyatn. i ee primen., 66:4 (2021), 718–733  mathnet  crossref
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