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41.
A fictitious domain approach to the numerical solution of PDEs in stochastic domains 总被引:1,自引:0,他引:1
We present an efficient method for the numerical realization of elliptic PDEs in domains depending on random variables. Domains
are bounded, and have finite fluctuations. The key feature is the combination of a fictitious domain approach and a polynomial
chaos expansion. The PDE is solved in a larger, fixed domain (the fictitious domain), with the original boundary condition
enforced via a Lagrange multiplier acting on a random manifold inside the new domain. A (generalized) Wiener expansion is
invoked to convert such a stochastic problem into a deterministic one, depending on an extra set of real variables (the stochastic
variables). Discretization is accomplished by standard mixed finite elements in the physical variables and a Galerkin projection
method with numerical integration (which coincides with a collocation scheme) in the stochastic variables. A stability and
convergence analysis of the method, as well as numerical results, are provided. The convergence is “spectral” in the polynomial
chaos order, in any subdomain which does not contain the random boundaries. 相似文献
42.
Tokuzo Shiga 《Probability Theory and Related Fields》1997,108(3):417-439
Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf;
d
in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate
the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ600;0.
Received: 21 May 1996 / In revised form: 2 February 1997 相似文献
43.
R. M. Dudley 《Probability Theory and Related Fields》1994,100(2):175-189
Summary In a separable metric space, if two Borel probability measures (laws) are nearby in a suitable metric, then there exist random variables with those laws which are nearby in probability. Specifically, by a well-known theorem of Strassen, the Prohorov distance between two laws is the infimum of Ky Fan distances of random variables with those laws. The present paper considers possible extensions of Strassen's theorem to two random elements one of which may be (compact) set-valued and/or non-measurable. There are positive results in finite-dimensional spaces, but with factors depending on the dimension. Examples show that such factors cannot entirely be avoided, so that the extension of Strassen's theorem to the present situation fails in infinite dimensions.This research was partially supported by a Guggenheim Fellowship, by National Science Foundation grant DMS 8505550 at MSRI-Berkeley, and other NSF grants 相似文献
44.
Summary As a continuation of the study by Herbst and Pitt (1991), this note presents two criteria. The first one is on the order-preservation for two (may be different) multidimensional diffusion processes. The second one is on the preservation of positive correlations for a diffusion process.Research supported in part by the Ying-Tung Fok Educational Foundation and the National Natural Science Foundation of China 相似文献
45.
Summary We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.Partially supported by ONR N00014-91-J-1010 相似文献
46.
Dmitrii S. Silvestrov 《Acta Appl Math》1994,34(1-2):109-124
Coupling procedures for Markov renewal processes are described. Applications to ergodic theorems for processes with semi-Markov switchings are considered.This paper was partly prepared with the support of NFR Grant F-UP 10257-300. 相似文献
47.
Partially supportted by Grant MM-22/1991 of MESC 相似文献
48.
Asymptotics in the random assignment problem 总被引:1,自引:0,他引:1
David Aldous 《Probability Theory and Related Fields》1992,93(4):507-534
Summary We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on the known numerical bounds for the limit.Research supported by NSF Grant MCS90-01710 相似文献
49.
Yuri Borovskikh 《Acta Appl Math》1994,35(3):213-298
U-statistics in Banach spaces are considered and thoroughly investigated. The martingale structure, estimates of moments, the law of large numbers, the central limit theorem, the invariance principle, estimates of the rate of convergence, and large deviations are established 相似文献
50.
Emrys A. Jones Nicholas P. Lockyer John C. Vickerman 《International journal of mass spectrometry》2007,260(2-3):146
Recent developments in desorption/ionisation mass spectrometry techniques have made their application to biological analysis a realistic and successful proposition. Developments in primary ion source technology, mainly through the advent of polyatomic ion beams, have meant that the technique of secondary ion mass spectrometry (SIMS) can now access the depths of information required to allow biological imaging to be a viable option.Here the role of the primary ion C60+ is assessed with regard to molecular imaging of lipids and pharmaceuticals within tissue sections. High secondary ion yields and low surface damage accumulation are demonstrated on both model and real biological samples, indicating the high secondary ion efficiency afforded to the analyst by this primary ion when compared to other cluster ion beams used in imaging. The newly developed 40 keV C60+ ion source allows the beam to be focused such that high resolution imaging is demonstrated on a tissue sample, and the greater yields allow the molecular signal from the drug raclopride to be imaged within tissue section following in vivo dosing.The localisation shown for this drug alludes to issues regarding the chemical environment affecting the ionisation probability of the molecule; the importance of this effect is demonstrated with model systems and the possibility of using laser post-ionisation as a method for reducing this consequence of bio-sample complexity is demonstrated and discussed. 相似文献