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The Measurable Space of Stochastic Processes

2010
*
2010 Seventh International Conference on the Quantitative Evaluation of Systems
*

*The*structural operational semantics associates to each

*process*a set

*of*

*measures*over

*the*

*space*

*of*

*processes*. ...

*The*set

*of*

*processes*is organised as a

*measurable*

*space*by

*the*sigma-algebra generated by structural congruence. ...

*The*novelty

*of*our approach derives firstly from

*the*structure

*of*

*the*

*measurable*

*space*

*of*

*stochastic*

*processes*. ...

##
###
The Measurability of a Stochastic Process of Second Order and its Linear Space

1975
*
Proceedings of the American Mathematical Society
*

As
a consequence
it is shown that a second
order

doi:10.2307/2039766
fatcat:ghqwrs6gd5hafcdk6f6wgk34hm
*process*is oscillatory if and only if its linear*space*is separable. 1.*The**measurability**of*a*stochastic**process**of*second order. ...*of**the**process*and*the*separability*of*its reproducing kernel Hilbert*space*or its linear*space*. ...##
###
The measurability of a stochastic process of second order and its linear space

1975
*
Proceedings of the American Mathematical Society
*

As
a consequence
it is shown that a second
order

doi:10.1090/s0002-9939-1975-0356206-9
fatcat:oro7w3gz7bdm3b4xratvc2qai4
*process*is oscillatory if and only if its linear*space*is separable. 1.*The**measurability**of*a*stochastic**process**of*second order. ...*of**the**process*and*the*separability*of*its reproducing kernel Hilbert*space*or its linear*space*. ...##
###
An improvement of the integrability of the state space of the Φ^4_3-process and the support of the Φ ^4_3-measure constructed by the limit of stationary processes of approximating stochastic quantization equations
[article]

2022
*
arXiv
*
pre-print

We improve

arXiv:2102.07303v2
fatcat:j4mhebqoxzblnij73bduqs74ue
*the*integrability*of**the*state*space**of**the*Φ ^4_3-*process*and*the*support*of**the*Φ ^4_3-*measure*on*the*torus obtained in [Albeverio, Kusuoka, Ann. Sc. Norm. Super. Pisa Cl. ... For*the*improvement, we improve*the*estimates*of**the*Hölder continuity in time*of**the*solutions to approximation equations. ...*The*author thanks*the*anonymous referees for helpful comments.*The*comments improved*the*quality*of**the*present paper. ...##
###
Stochastic post-processing of the deterministic boundary element modelling of the transient electric field from GPR dipole antenna propagating through lower half-space

2017
*
International Journal of Computational Methods & Experimental Measurements
*

*The*paper deals with time domain-deterministic

*stochastic*assessment

*of*a transient electric field generated by a ground penetrating radar (GPR) dipole antenna and transmitted into a lower half-

*space*. ...

*The*Hallen equation is solved via

*the*Galerkin-Bubnov variant

*of*

*the*Indirect Boundary Element Method (GB-IBEM) and

*the*

*space*-time current distribution along

*the*dipole antenna is obtained, thus providing ... ACKNOWLEDGEMENT This work benefited from networking activities was carried out within

*the*EU funded COST Action TU1208 "Civil Engineering Applications

*of*Ground Penetrating Radar." ...

##
###
A New General Approach to Vector Valued Stochastic Integration

2014
*
International Journal of Modeling and Optimization
*

With such an approach, we will explore

doi:10.7763/ijmo.2014.v4.389
fatcat:5ney6icof5bjbnj3pbxg3bytoi
*the*possible extension*of**the*theory*of**stochastic*integration to*the*more general setting*of*integrable*processes*taking values in normed vector*spaces*. ... We show that our approach makes applications possible to*stochastic**processes*that are not necessarily square integrable, nor even*measurable*. ... Let be a normed vector*space*and let a*measure**space*Ω, Σ, μ , be given. We denote by **the*outer-*measure*obtained by*the*Carathéodory extension*of**the**measure*\mu to*the*whole*of**the*power set 2 Ω . ...##
###
Page 5707 of Mathematical Reviews Vol. , Issue 2001H
[page]

2001
*
Mathematical Reviews
*

*The*concept allows

*the*author to recast and generalize

*the*whole

*stochastic*integration theory for Banach-

*space*-valued

*processes*using

*the*extensions

*of*vector

*measure*theory, and this is done with some ... Appl. (5) 22 (1998), 129-164; MR 2000h:60060]

*the*first author studied

*the*

*stochastic*integral

*of*

*process*

*measures*with values in a Banach

*space*E with integrable variation or semi- variation. ...

##
###
Gaussian measures on Orlicz spaces and abstract Wiener spaces

1986
*
Journal of Multivariate Analysis
*

Wutanabe Gaussian

doi:10.1016/0047-259x(86)90101-6
fatcat:hljzx3npa5bgroa7pk5svjpbym
*measures*on some non-Banach*spaces**of**measurable*functions are investigated. ...*The*main result is that every Gaussian*measure*on a separable Orlicz*space*L, is an extension*of**the*canonical cylindrical Gaussian distribution on*the*RKHS. ... So for a given*measurable**stochastic*It6 proved [ 131 that when a*stochastic**process*is defined on a standard Bore1*space**the*canonical modification*of*it is a*measurable**stochastic**process*. ...##
###
FUNCTIONAL ABSTRACTIONS OF STOCHASTIC HYBRID SYSTEMS

2006
*
IFAC Proceedings Volumes
*

A new concept

doi:10.3182/20060607-3-it-3902.00031
fatcat:mamg3gjjdzh2hnlyqz3ioijlze
*of**stochastic*bisimulation is introduced and its connection with equivalence*of**stochastic**processes*is established. ... Concepts*of*abstractions for*stochastic*hybrid systems are needed to ease*the**stochastic*reachability analysis. ... Applying this function to*the*paths*of**stochastic**process*that constitutes*the*SHS realization gives rise to a new*stochastic**process*with*the*state*space*in*the*real line. ...##
###
Space-time stochastic processes

1987
*
Stochastic Processes and their Applications
*

Using

doi:10.1016/0304-4149(87)90108-6
fatcat:frz4y4ci7jerfg5jyg7o2p6lra
*the*theory*of*algebraic representations*of*discrete time*stochastic**processes*in Johnson [1, 2, 3] , we describe: (1) how to estimate*the*algebraic representation*of**the*general*space*-time*stochastic*...*Space*-Time*Stochastic**Processes*Dudley Paul Johnson, University*of*Calgary, Canada In conducing a scientific experiment, one gets a sequence*of**measurements*[X(n), T(x)] where X(n) is a random variable ...*The*problem*of*getting explicit forms for such*measures*has been an open one for*the*last ten years, even in*the*simplest cases when*the*convex polygon is a square or a triangle. ...##
###
Page 1333 of Mathematical Reviews Vol. , Issue 2000b
[page]

2000
*
Mathematical Reviews
*

*The*

*stochastic*integral

*of*a predictable L?

*process*Z with respect to

*the*Gaussian martingale

*measure*M defines a new martingale

*measure*M%. ... Associated with

*the*

*stochastic*

*process*W” there is an abstract Wiener

*space*(W,#;, Py), where Py is

*the*law

*of*W” on

*the*

*space*

*of*continuous paths W and

*the*Cameron-Martin

*space*Hy is

*the*image

*of*L7({ ...

##
###
Stochastic processes as Fourier transforms of stochastic measures

1975
*
Annales Academiae Scientiarum Fennicae Series A I Mathematica
*

In chapter 3 we give a modified definition

doi:10.5186/aasfm.1975.591
fatcat:dlfcytxwwjeajkfg4czyhjftyy
*of*a 7 -bounded*stochastic*Ann. Acad. Sci. Fennicre A. I. 591*process*and*of*a harmonizable*stochastic**process*, based on*the*use*of*Raclon*measures*. ... A*stochastic**process*r: R "> LllP) is called, harmonizable iJ its coaari,ance function can be represented, i,n*the*form bounded*stochastic**process*is*the*Fourier transform*of*a boundecl*stochastic**measure*...##
###
Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises

2013
*
Abstract and Applied Analysis
*

Some fundamental properties

doi:10.1155/2013/653160
fatcat:z6oarbeutfg5lerin6vzloprt4
*of*a subordinator Lévy*process*and*the**stochastic*integral with respect to a Lévy*process*are discussed, and then*the*existence, uniqueness, regularity, and*the*random dynamical ... This paper is devoted to*the*investigation*of*random dynamics*of**the**stochastic*Boussinesq equations driven by Lévy noise. ... Supported by*the*NSF*of*China (no. 10971225, no. 11028102, no. 11271013, and no. 91130003),*the*SRF for ROCS, SEM, and*the*NSF Grant 1025422. ...##
###
Page 741 of Annals of Mathematics Vol. 41, Issue 4
[page]

1940
*
Annals of Mathematics
*

Random Functions and

*Measurable**Stochastic**Processes*In*the*formulation*of**the*theory*of**stochastic**processes*a fundamental notion is that*of*a*measurable**stochastic**process*." ... If 2 is any*stochastic**process*, then in terms*of*P-*measure*on 2 and Lebesgue*measure*on 7’ we can define a*measure*on*the*product*space*7’ X © in*the*usual (multiplicative) way; we suppose also that this ...##
###
Page 5010 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

These

*spaces*are useful for describing infinite-dimensional second-order*stochastic**processes*. They play*the*same role as*the**space**of*Hilbert-Schmidt operators on a Hilbert*space*. ... Summary: “For a random function depending on time and on a point*of*a*measure**space*, we find an asymptotic expression for*the**measure**of**the*region in which*the*values*of**the*function do not exceed a given ...
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