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The Measurable Space of Stochastic Processes

Luca Cardelli, Radu Mardare
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

Stamatis Cambanis
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

Stamatis Cambanis
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]

Seiichiro Kusuoka
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

D. Poljak, S. Sesnic, S. Lallechere, K. el Khamlichi Drissi
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

Mangatiana A. Robdera
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

Anna T Lawniczak
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

Manuela L. Bujorianu, Henk A.P. Blom, Holger Hermanns
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

Dudley Paul Johnson
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

Hannu Niemi
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

Jianhua Huang, Yuhong Li, Jinqiao Duan
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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