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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. ...
doi:10.1109/qest.2010.30
dblp:conf/qest/CardelliM10
fatcat:rnxsy2igdvfdbjqwpyq3anlqhi
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 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. ...
doi:10.2307/2039766
fatcat:ghqwrs6gd5hafcdk6f6wgk34hm
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 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. ...
doi:10.1090/s0002-9939-1975-0356206-9
fatcat:oro7w3gz7bdm3b4xratvc2qai4
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 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. ...
arXiv:2102.07303v2
fatcat:j4mhebqoxzblnij73bduqs74ue
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." ...
doi:10.2495/cmem-v5-n5-678-685
fatcat:23qec5ssejgftlgbed7ons72ii
A New General Approach to Vector Valued Stochastic Integration
2014
International Journal of Modeling and Optimization
With such an approach, we will explore 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 . ...
doi:10.7763/ijmo.2014.v4.389
fatcat:5ney6icof5bjbnj3pbxg3bytoi
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 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. ...
doi:10.1016/0047-259x(86)90101-6
fatcat:hljzx3npa5bgroa7pk5svjpbym
FUNCTIONAL ABSTRACTIONS OF STOCHASTIC HYBRID SYSTEMS
2006
IFAC Proceedings Volumes
A new concept 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. ...
doi:10.3182/20060607-3-it-3902.00031
fatcat:mamg3gjjdzh2hnlyqz3ioijlze
Space-time stochastic processes
1987
Stochastic Processes and their Applications
Using 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. ...
doi:10.1016/0304-4149(87)90108-6
fatcat:frz4y4ci7jerfg5jyg7o2p6lra
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 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 ...
doi:10.5186/aasfm.1975.591
fatcat:dlfcytxwwjeajkfg4czyhjftyy
Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises
2013
Abstract and Applied Analysis
Some fundamental properties 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. ...
doi:10.1155/2013/653160
fatcat:z6oarbeutfg5lerin6vzloprt4
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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