A note on stochastic processes with independent increments taking values in an abelian group

It is well known that any stochastically continuous real valued stochastic process with independent increments defined on a compact time interval can be decomposed into a sum of independent processes, one of which is Gaussian with continuous sample paths, and the remainder of which have sample paths which are continuous except at a finite number of points with the discontinuities occurring at Poisson time points. The purpose of this note is to announce a proof of the above theorem in the case where the process takes values in an abelian group G. The detailed proof will appear elsewhere. The basic ideas of the proof in the case when G is finite dimensional Euclidean space are contained in Chapter VI of Gikhman and Skorohod (1965).

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On targeting an integral funnel of control system at a target set in the phase space

10.35634/2226-3594-2020-56-07 ◽

2020 ◽

Vol 56 ◽

pp. 79-101

Author(s):

V.N. Ushakov ◽

A.V. Ushakov

Keyword(s):

Exact Solution ◽

Control System ◽

Phase Space ◽

Euclidean Space ◽

Time Moment ◽

Dimensional Euclidean Space ◽

Time Interval ◽

Finite Dimensional ◽

Approximate Construction ◽

Target Set

A control system in finite-dimensional Euclidean space is considered. On a given time interval, we investigate the problem of constructing an integral funnel for which a section corresponding to the last time moment of interval is equal to a target set in a phase space. Since the exact solution of such a funnel is possible only in rare cases, the question of the approximate construction of an integral funnel is being studied.

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Stochastic Processes with Independent Increments Taking Values in an Abelian Group

Proceedings of the London Mathematical Society ◽

10.1112/plms/s3-22.3.507 ◽

1971 ◽

Vol s3-22 (3) ◽

pp. 507-530 ◽

Cited By ~ 4

Author(s):

M. S. Bingham

Keyword(s):

Abelian Group ◽

Stochastic Processes ◽

Independent Increments ◽

Processes With Independent Increments

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CONTROL SYSTEM DEPENDING ON A PARAMETER

Ural mathematical journal ◽

10.15826/umj.2021.1.011 ◽

2021 ◽

Vol 7 (1) ◽

pp. 120

Author(s):

Vladimir N. Ushakov ◽

Aleksandr A. Ershov ◽

Andrey V. Ushakov ◽

Oleg A. Kuvshinov

Keyword(s):

Control System ◽

Phase Space ◽

Specific Problem ◽

Dimensional Euclidean Space ◽

Time Interval ◽

Two Dimensional ◽

Finite Time Interval ◽

Finite Dimensional ◽

Dimensional Phase Space ◽

Target Set

A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.

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Utilization of remote sensing for estimation of scale of cutting and growing of forest zones

Geodesy and Cartography ◽

10.22389/0016-7126-2017-920-2-57-60 ◽

2017 ◽

Vol 920 (2) ◽

pp. 57-60

Author(s):

F.E. Guliyeva

Keyword(s):

Remote Sensing ◽

Fixed Time ◽

Time Interval ◽

Time Points ◽

Average Value ◽

Time Period ◽

Remote Estimation ◽

The Given ◽

Forest Cutting

The study of results of relevant works on remote sensing of forests has shown that the known methods of remote estimation of forest cuts and growth don’t allow to calculate the objective average value of forests cut volume during the fixed time period. The existing mathematical estimates are not monotonous and make it possible to estimate primitively the scale of cutting by computing the ratio of data in two fixed time points. In the article the extreme properties of the considered estimates for deforestation and reforestation models are researched. The extreme features of integrated averaged values of given estimates upon limitations applied on variables, characterizing the deforestation and reforestation processes are studied. The integrated parameter, making it possible to calculate the averaged value of estimates of forest cutting, computed for all fixed time period with a fixed step is suggested. It is shown mathematically that the given estimate has a monotonous feature in regard of value of given time interval and make it possible to evaluate objectively the scales of forest cutting.

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On Vitali's Theorem for Groups of Motions of Euclidean Space

Georgian Mathematical Journal ◽

10.1515/gmj.1999.323 ◽

1999 ◽

Vol 6 (4) ◽

pp. 323-334

Author(s):

A. Kharazishvili

Keyword(s):

Euclidean Space ◽

Dimensional Euclidean Space ◽

Finite Dimensional

Abstract We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [Sul problema della misura dei gruppi di punti di una retta, 1905] holds true. This characterization is formulated in purely geometrical terms.

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Global sensitivity analysis for stochastic processes with independent increments

Probabilistic Engineering Mechanics ◽

10.1016/j.probengmech.2020.103098 ◽

2020 ◽

Vol 62 ◽

pp. 103098

Author(s):

Emeline Gayrard ◽

Cédric Chauvière ◽

Hacène Djellout ◽

Pierre Bonnet ◽

Don-Pierre Zappa

Keyword(s):

Sensitivity Analysis ◽

Stochastic Processes ◽

Global Sensitivity Analysis ◽

Global Sensitivity ◽

Independent Increments ◽

Processes With Independent Increments

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Limit Distribution of the Exit Time From an Expanding Interval and of the Position at Exit Time of a Process with Independent Increments and One-Signed Jumps

Theory of Probability and Its Applications ◽

10.1137/1123046 ◽

1979 ◽

Vol 23 (2) ◽

pp. 402-407

Author(s):

V. M. Shurenkov

Keyword(s):

Limit Distribution ◽

Exit Time ◽

Process With Independent Increments ◽

Independent Increments

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Radiomorphology of the Habib Sealer-Induced Resection Plane during Long-Time Followup:A Longitudinal Single Center Experience after 64 Radiofrequency-AssistedLiver Resections

HPB Surgery ◽

10.1155/2010/403097 ◽

2010 ◽

Vol 2010 ◽

pp. 1-7 ◽

Cited By ~ 4

Author(s):

Robert Kleinert ◽

Roger Wahba ◽

Christoph Bangard ◽

Klaus Prenzel ◽

Arnulf H. Hölscher ◽

...

Keyword(s):

Liver Resection ◽

Morphological Characteristics ◽

Postoperative Mortality ◽

Coagulation Necrosis ◽

Time Interval ◽

Safe Alternative ◽

Time Points ◽

Single Center Experience ◽

Long Time

Background. Radiofrequency (RF-) assisted liver resection devices like the Habib sealer induce a necrotic resection plane from which a small margin of necrotic liver tissue remains in situ. The aim of the present paper was to report our long-time experience with the new resection method and the morphological characteristics of the remaining necrotic resection plane. Methods. 64 RF-assisted liver resections were performed using the Habib sealer. Followup was assessed at defined time points. Results. The postoperative mortality was 3,6% and morbidity was 18%. The followup revealed that the necrotic zone was detectable in all analyzed CT and MRI images as a hypodense structure without any contrast enhancement at all time points, irrespectively of the time interval between resection and examination. Conclusion. Liver resection utilizing radiofrequency-induced resection plane coagulation is a safe alternative to the established resection techniques. The residual zone of coagulation necrosis remains basically unchanged during a followup of three years. This has to be kept in mind when evaluating the follow up imaging of these patients.

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On inequalities of the Tchebychev type

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100002085 ◽

1963 ◽

Vol 59 (1) ◽

pp. 135-146 ◽

Cited By ~ 11

Author(s):

J. F. C. Kingman

Keyword(s):

Probability Theory ◽

Euclidean Space ◽

Random Variable ◽

Dimensional Euclidean Space ◽

Real Random Variable ◽

Finite Dimensional

1. A type of problem which frequently occurs in probability theory and statistics can be formulated in the following way. We are given real-valued functions f(x), gi(x) (i = 1, 2, …, k) on a space (typically finite-dimensional Euclidean space). Then the problem is to set bounds for Ef(X), where X is a random variable taking values in , about which all we know is the values of Egi(X). For example, we might wish to set bounds for P(X > a), where X is a real random variable with some of its moments given.

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