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1

Stochastic differential inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1997
|
tom 17
|
nr 1-2
51-65
EN
The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.
2

Viability theorems for stochastic inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
|
tom 15
|
nr 1
61-42
EN
Sufficient conditions for the existence of solutions to stochastic inclusions $x_t - x_s ∈ ∫^t_s F_τ(x_τ)dτ + ∫^t_s G_τ(x_τ)dw_τ + ∫^t_s∫_{IRⁿ} H_{τ,z}(x_τ)ν̃ (dτ,dz)$ beloning to a given set K of n-dimensional cádlág processes are given.
3
Content available remote

Canonical correlation analysis for functional data

100%
Krzyśko M., Waszak Ł.
Biometrical Letters
|
2013
|
tom 50
|
nr 2
95-105
EN
Classical canonical correlation analysis seeks the associations between two data sets, i.e. it searches for linear combinations of the original variables having maximal correlation. Our task is to maximize this correlation, and is equivalent to solving a generalized eigenvalue problem. The maximal correlation coefficient (being a solution of this problem) is the first canonical correlation coefficient. In this paper we propose a new method of constructing canonical correlations and canonical variables for a pair of stochastic processes represented by a finite number of orthonormal basis functions.
4

Stochastic differential inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1999
|
tom 19
|
nr 1-2
123-129
EN
The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.
5
Content available remote

Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients S2−almost automorphic

88%
Mbaye M. M.
Nonautonomous Dynamical Systems
|
2016
|
tom 3
|
nr 1
85-103
EN
In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S2−almost automorphic) processes in distribution. We establish some interesting results on the functional space of such processes like an composition theorems. Next, under some suitable assumptions, we establish the existence, the uniqueness and the stability of the square-mean almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Lévy noise in case when the functions forcing are both continuous and S2−almost automorphic. We provide an example to illustrate ours results.
6
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Study with George Styan

75%
Bertrand P.
Discussiones Mathematicae Probability and Statistics
|
2013
|
tom 33
|
nr 1-2
41-46
EN
George Styan and I first met when he came to the University of Birmingham to study Mathematics. We both developed interests in Mathematical Statistics. Matrix theory is an essential component of such courses and we both excelled at it. Our paths have intersected on a number of occasions and George's insight and cooperation has been a great help in enabling me to carry out research in several areas. This article summarizes the value of George's presence and help in carrying out some interesting and complicated research projects.
7
Content available remote

Statistical estimation of higher-order spectral densities by means of general tapering

63%
M'hammed Baba Harra
Applicationes Mathematicae
|
1996-1997
|
tom 24
|
nr 4
357-381
EN
Given a realization on a finite interval of a continuous-time stationary process, we construct estimators for higher order spectral densities. Tapering and shift-in-time methods are used to build estimators which are asymptotically unbiased and consistent for all admissible values of the argument. Asymptotic results for the fourth-order densities are given. Detailed attention is paid to the nth order case.
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