B. A. Rogozin, “The distribution of the first hit for stable and asymptotically stable walks on an interval”, Teor. Veroyatnost. i Primenen., 17:2 (1972), 342–349; Theory Probab. Appl., 17:2 (1973), 332

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Teoriya Veroyatnostei i ee Primeneniya, 1972, Volume 17, Issue 2, Pages 342–349 (Mi tvp2589)

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

Short Communications

The distribution of the first hit for stable and asymptotically stable walks on an interval

B. A. Rogozin

Novosibirsk

Full-text PDF (375 kB) Citations (34)

Abstract: Let

$\{\xi(t);t\ge0\}$ be a strongly stable process,

$\tau=\inf\{t\colon\xi(t)\notin[0,1]\}$ .
Formulas for

$\mathbf P\{1\le\xi(\tau)<1+y\mid\xi(0)=x\}$ , and

$\mathbf P\{0\ge\xi(\tau)>-y\mid\xi(0)=x\}$ ,

$0\le x\le1$ ,

$y\ge0$ , are derived and applied to random walks.

Received: 26.11.1970

English version:
Theory of Probability and its Applications, 1973, Volume 17, Issue 2, Pages 332–338
DOI: https://doi.org/10.1137/1117035

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: B. A. Rogozin, “The distribution of the first hit for stable and asymptotically stable walks on an interval”, Teor. Veroyatnost. i Primenen., 17:2 (1972), 342–349; Theory Probab. Appl., 17:2 (1973), 332–338

Citation in format AMSBIB

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\by B.~A.~Rogozin

\paper The distribution of the first hit for stable and asymptotically stable walks on an interval

\jour Teor. Veroyatnost. i Primenen.

\yr 1972

\vol 17

\issue 2

\pages 342--349

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=300349}

\zmath{https://zbmath.org/?q=an:0272.60050}

\transl

\jour Theory Probab. Appl.

\yr 1973

\vol 17

\issue 2

\pages 332--338

\crossref{https://doi.org/10.1137/1117035}

Linking options:

https://www.mathnet.ru/eng/tvp2589

https://www.mathnet.ru/eng/tvp/v17/i2/p342

This publication is cited in the following 34 articles:

Kees van Schaik, Alexander R. Watson, Xin Xu, “Optimal stopping of the stable process with state-dependent killing”, Bernoulli, 31:1 (2025)
Alexander R. Watson, “A growth-fragmentation model connected to the ricocheted stable process”, J. Appl. Probab., 60:2 (2023), 493
Jacek Mucha, “Spectral theory for one-dimensional (non-symmetric) stable processes killed upon hitting the origin”, Electron. J. Probab., 26:none (2021)
Leif Döring, Andreas E. Kyprianou, “Entrance and exit at infinity for stable jump diffusions”, Ann. Probab., 48:3 (2020)
Asem Wardak, “First passage leapovers of Lévy flights and the proper formulation of absorbing boundary conditions”, J. Phys. A: Math. Theor., 53:37 (2020), 375001
Leif Döring, Andreas E. Kyprianou, Philip Weissmann, “Stable processes conditioned to avoid an interval”, Stochastic Processes and their Applications, 130:2 (2020), 471
Leif Döring, Alexander R. Watson, Philip Weissmann, “Lévy processes with finite variance conditioned to avoid an interval”, Electron. J. Probab., 24:none (2019)
Fatih Dinc, “Analytical estimation for the impulse response of an n-dimensional diffusion channel with an absorbing receiver”, J. Phys. A: Math. Theor., 52:11 (2019), 11LT01
Pierre Lenthe, Philip Weissmann, “Completely asymmetric stable processes conditioned to avoid an interval”, J. Appl. Probab., 56:4 (2019), 1187
Julien Letemplier, Thomas Simon, “On the law of homogeneous stable functionals”, ESAIM: PS, 23 (2019), 82
Kyprianou A.E., Vakeroudis S.M., “Stable Windings At the Origin”, Stoch. Process. Their Appl., 128:12 (2018), 4309–4325
Andreas E. Kyprianou, “Deep factorisation of the stable process”, Electron. J. Probab., 21:none (2016)
Bartłomiej Dybiec, Ewa Gudowska-Nowak, Aleksei Chechkin, “To hit or to pass it over—remarkable transient behavior of first arrivals and passages for Lévy flights in finite domains”, J. Phys. A: Math. Theor., 49:50 (2016), 504001
Christophe Profeta, Thomas Simon, Lecture Notes in Mathematics, 2168, Séminaire de Probabilités XLVIII, 2016, 325
Kolokoltsov V., “on Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equations”, Fract. Calc. Appl. Anal., 18:4 (2015), 1039–1073
A. E. Kyprianou, A. R. Watson, Lecture Notes in Mathematics, 2123, Séminaire de Probabilités XLVI, 2014, 333
Andreas E. Kyprianou, Juan Carlos Pardo, Alexander R. Watson, “Hitting distributions of $\alpha$ -stable processes via path censoring and self-similarity”, Ann. Probab., 42:1 (2014)
Andreas E. Kyprianou, Universitext, Fluctuations of Lévy Processes with Applications, 2014, 197
A. E. Kyprianou, J. C. Pardo, A. R. Watson, “The extended hypergeometric class of Lévy processes”, Journal of Applied Probability, 51:A (2014), 391
Andreas E. Kyprianou, Universitext, Fluctuations of Lévy Processes with Applications, 2014, 231

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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