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2010 Mathematics Subject Classification index

https://doi.org/10.15559/16-VMSTA34MI

Pub. online: 4 Jan 2017 Type: 2010 Mathematics Subject Classification Index

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 4 (2016), pp. 369–372

2010 Mathematics Subject Classification index

https://doi.org/10.15559/16-MSTA34MI

Pub. online: 4 Jan 2017 Type: 2010 Mathematics Subject Classification Index

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 4 (2016), pp. 369–372

Subject index

https://doi.org/10.15559/16-VMSTA34SI

Pub. online: 4 Jan 2017 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 4 (2016), pp. 367–368

Subject index

https://doi.org/10.15559/16-MSTA34SI

Pub. online: 4 Jan 2017 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 4 (2016), pp. 367–368

Author index

https://doi.org/10.15559/16-VMSTA34AI

Pub. online: 4 Jan 2017 Type: Author Index

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 4 (2016), p. 365

Author index

https://doi.org/10.15559/16-MSTA34AI

Pub. online: 4 Jan 2017 Type: Author Index

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 4 (2016), p. 365

Description of the symmetric convex random closed sets as zonotopes from their Feret diameters

Saïd Rahmani Jean-Charles Pinoli Johan Debayle

https://doi.org/10.15559/16-VMSTA70

Pub. online: 3 Jan 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 4 (2016), pp. 325–364

Abstract

In this paper, the 2-D random closed sets (RACS) are studied by means of the Feret diameter, also known as the caliper diameter. More specifically, it is shown that a 2-D symmetric convex RACS can be approximated as precisely as we want by some random zonotopes (polytopes formed by the Minkowski sum of line segments) in terms of the Hausdorff distance. Such an approximation is fully defined from the Feret diameter of the 2-D convex RACS. Particularly, the moments of the random vector representing the face lengths of the zonotope approximation are related to the moments of the Feret diameter random process of the RACS.

Description of the symmetric convex random closed sets as zonotopes from their Feret diameters

Saïd Rahmani Jean-Charles Pinoli Johan Debayle

https://doi.org/10.15559/16-MSTA70

Pub. online: 3 Jan 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 4 (2016), pp. 325–364

Abstract

An estimate for an expectation of the simultaneous renewal for time-inhomogeneous Markov chains

Vitaliy Golomoziy

https://doi.org/10.15559/16-VMSTA68

Pub. online: 23 Dec 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 4 (2016), pp. 315–323

Abstract

In this paper, we consider two time-inhomogeneous Markov chains ${X_{t}^{(l)}}$, $l\in \{1,2\}$, with discrete time on a general state space. We assume the existence of some renewal set C and investigate the time of simultaneous renewal, that is, the first positive time when the chains hit the set C simultaneously. The initial distributions for both chains may be arbitrary. Under the condition of stochastic domination and nonlattice condition for both renewal processes, we derive an upper bound for the expectation of the simultaneous renewal time. Such a bound was calculated for two time-inhomogeneous birth–death Markov chains.

An estimate for an expectation of the simultaneous renewal for time-inhomogeneous Markov chains

Vitaliy Golomoziy

https://doi.org/10.15559/16-MSTA68

Pub. online: 23 Dec 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 4 (2016), pp. 315–323

Abstract

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