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Stochastic Geometry

2019
Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications ...
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Stochastic Differential Geometry

2021
Semi-martingales, bilinear forms, pull-back, covariation process, semimartingale integral, connection, chain rule, differential operators and Christoffel symbols, martingale criteria, induced connections, affine and convex maps, geodesics and martingale criteria, local drift and diffusion rates, sub-manifolds and projection, diffusions, Riemannian ...
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Stochastic Geometry and Its Applications.

Journal of the American Statistical Association, 1988
23. Stochastic Geometry and its Applications. By D. Stoyan, W. S. Kendall and J. Mecke. ISBN 0 471 90519 4. Wiley, 1987. 345p. £23.50. (Wiley Series in Probability and Mathematical Statistics. A co‐production with Akademie‐Verlag, GDR.)
B. D. Ripley   +3 more
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Stochastic differential geometry

Russian Mathematical Surveys, 1983
The paper gives another exposition of what is now called ''Malliavin's stochastic calculus''. The approach is somewhat close to the Bismut's one. The results are extended to the case of diffusion processes on infinite dimensional smooth manifolds. This enables the author to construct certain quasi-invariant measures on infinite dimensional Lie groups ...
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Stochastic geometry

1992
Abstract So far we have considered random countable subsets of spaces S which have always been subsets of !Rd for some dimension d. The theory is, however, much more general, and applies to random structures which look quite different from the irregular array of isolated points depicted in Fig. 1.1.
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Stochastic differential geometry: An introduction

Acta Applicandae Mathematicae, 1987
This is a survey on the relations between asymptotic properties of semi- martingales and, in particular, of Brownian motion on a Riemannian manifold on the one hand and curvature properties of the manifold on the other hand. Following a brief description of real-valued semimartingales and of some essentials of calculus on manifolds, an introduction to ...
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Some Stochastic Geometry

1996
We begin with a review of some basic definitions and ideas from probability theory. The reader wishing a more detailed description of the tools that will be necessary can consult [43].
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Models of stochastic geometry ? A survey

ZOR Zeitschrift f� Operations Research Methods and Models of Operations Research, 1993
Summary: This paper discusses some models of stochastic geometry which are of potential interest for operations research. These are the Boolean model, a certain model for random compact sets and marked point processes. The Boolean model is a generalization of the well-known queueing system \(M/G/\infty\).
Stoyan, Dietrich, Lippmann, Günter
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Stochastic Differential Geometry

2008
Abstract The chapter further develops the theory of (non-degenerate) diffusion processes, considered as existing on an arbitrary manifold ℳ, from the point of view of stochastic differential geometry. In this description the diffusion tensor plays an essential underlying role in supplying the metrical structure of the manifold.
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Stereology and Stochastic Geometry

International Statistical Review / Revue Internationale de Statistique, 1990
In the last ten years stereology has drastically changed its state, and it seems that this process will continue in the future. This applies to its practical methods as well as to its theoretical fundamentals. Thus it may be justified to publish now a further review paper on stereology in this journal, following the papers by Ripley (1984) and Jensen ...
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