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Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1976
and computed the second moment of the difference of the expressions in (1) and (2). In this paper, by examining the excursions in Brownian motion and using a new formula for the distribution of their maxima, we obtain a direct identification of the limit in (1) without using (2). Let Tx=inf{t: W(t )=x} , Tx=inf{t: Y( t )=x} . For a > 0 let R~=0, R~= T/,
Chung, Kai Lai, Durrett, Richard
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and computed the second moment of the difference of the expressions in (1) and (2). In this paper, by examining the excursions in Brownian motion and using a new formula for the distribution of their maxima, we obtain a direct identification of the limit in (1) without using (2). Let Tx=inf{t: W(t )=x} , Tx=inf{t: Y( t )=x} . For a > 0 let R~=0, R~= T/,
Chung, Kai Lai, Durrett, Richard
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On the local time process standardized by the local time at zero
Acta Mathematica Hungarica, 1988Let L(a,t) be the (jointly continuous) local time of a Wiener process. The following iterated logarithm law is proved: For \(a\in R\) and \(\alpha\leq 1/2\) \[ \limsup_{t\to \infty}\frac{| L(a,t)- L(0,t)|}{t^{(1-2\alpha)/4}(L(0,t)\quad)^{\alpha}(\log \log t)^{(3-2\alpha)/4}}=| a|^{1/2}K_{\alpha}\quad a.s. \] with explicitly given \(K_{\alpha}\).
Csáki, E., Földes, A.
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Russian Mathematical Surveys, 1989
The local time of a Brownian motion occupies a special place in the theory of local times of stochastic processes. Among the reasons for this are, first, the fact that it allows the construction of a theory very rich in content and, second, that in its example we can see features of the behavior of local times of more general processes, in particular ...
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The local time of a Brownian motion occupies a special place in the theory of local times of stochastic processes. Among the reasons for this are, first, the fact that it allows the construction of a theory very rich in content and, second, that in its example we can see features of the behavior of local times of more general processes, in particular ...
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1996
We now take up the fine structure of the local time t(t) = t(t 0) and its inverse function t-1(t) for a persistent non-singular diffusion D* on an interval Q containing 0 as an inside point or as a left end point, with — u+(0) + m(0) (Gu)(0) = 0 in the second case. A number of the statements made below hold for transient diffusions also (see esp.
Kiyosi Itô, Henry P. McKean
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We now take up the fine structure of the local time t(t) = t(t 0) and its inverse function t-1(t) for a persistent non-singular diffusion D* on an interval Q containing 0 as an inside point or as a left end point, with — u+(0) + m(0) (Gu)(0) = 0 in the second case. A number of the statements made below hold for transient diffusions also (see esp.
Kiyosi Itô, Henry P. McKean
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Space-time localization using times of arrival
2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2011We provide a computationally efficient framework for utilizing Time of Arrival (ToA) sensors to localize multiple events in close proximity in space and time. Conventional ToA-based localization algorithms are typically designed for single events. Na¨ive approaches for associating ToAs with events and then applying a conventional localization algorithm
Sriram Venkateswaran, Upamanyu Madhow
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Locally Time Homogeneous Time Series Modelling
2009In this paper three locally adaptive estimation methods are applied to the problems of variance forecasting, value-at-risk analysis and volatility estimation within the context of nonstationary financial time series. A general procedure for the computation of critical values is given.
Elagin, Mstislav, Spokoiny, Vladimir
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Space-Time Localization and Mapping
2017 IEEE International Conference on Computer Vision (ICCV), 2017This paper addresses the problem of building a spatiotemporal model of the world from a stream of time-stamped data. Unlike traditional models for simultaneous localization and mapping (SLAM) and structure-from-motion (SfM) which focus on recovering a single rigid 3D model, we tackle the problem of mapping scenes in which dynamic components appear ...
Minhaeng Lee, Charless C. Fowlkes
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Local time as a derivative of occupation times
1965Made available in DSpace on 2014-12-09T22:17:24Z (GMT). No. of bitstreams: 1 6604190.pdf: 1210328 bytes, checksum: a7bb08b2abe8bf9efa914578800eb8bb (MD5) Previous issue date: 1965 ; Embargo set by: Seth Robbins for item 61719 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs ; Restricted to ...
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Brownian Local Time of the Second Order at the Inverse Local Time Moment
Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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