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Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 4, Pages 798–812 (Mi tvp3663)  

This article is cited in 5 scientific papers (total in 5 papers)

On local times for functions and stochastic processes. I

F. S. Nasyrov

Ufa State Aviation Technical University

Abstract: Let $X(t)$, $0\le t\le 1$, be a real-valued measurable function having a local time $\alpha (t,u)$, $0\le t\le 1$, $u\in\mathbf{R}$. If the latter is continuous in $t$ for a.e. $u$, then the distribution. $F(t,x)=\int_\mathbf{R}\mathbb{I}(\alpha(t,u)>x) du$ and the monotone rearrangement $\alpha^*(t,u)=\inf\{x:F(t,x)<u\}$ of the local time $\alpha(t,u)$ are the local times for $\xi(s)=\alpha(s,X(s))$ and $\xi^*(s)=F(s,X(s))$, $0\le s\le 1$, respectively.

Keywords: local time, distribution and monotone rearrangement of a function, orthogonal decomposition, Brownian motion.

Full text: PDF file (812 kB)

English version:
Theory of Probability and its Applications, 1995, 40:4, 702–713

Bibliographic databases:

Received: 06.12.1991

Citation: F. S. Nasyrov, “On local times for functions and stochastic processes. I”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 798–812; Theory Probab. Appl., 40:4 (1995), 702–713

Citation in format AMSBIB
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\by F.~S.~Nasyrov
\paper On local times for functions and stochastic processes.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 4
\pages 798--812
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1405146}
\zmath{https://zbmath.org/?q=an:0909.60057}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 4
\pages 702--713
\crossref{https://doi.org/10.1137/1140079}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WD22100009}


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    This publication is cited in the following articles:
    1. F. S. Nasyrov, “Generalized Lebesgue decomposition of continuous functions”, Math. Notes, 61:3 (1997), 376–379  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. F. S. Nasyrov, “Symmetric Integrals and Their Application in Financial Mathematics”, Proc. Steklov Inst. Math., 237 (2002), 256–269  mathnet  mathscinet  zmath
    3. F. S. Nasyrov, “Symmetric integrals and stochastic analysis”, Theory Probab. Appl., 51:3 (2007), 486–503  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. F. S. Nasyrov, “Ob obobschennoi formule Tanaki”, Ufimsk. matem. zhurn., 1:1 (2009), 69–76  mathnet  zmath
    5. Theory Probab. Appl., 57:2 (2013), 196–208  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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