共查询到20条相似文献,搜索用时 15 毫秒
1.
Markov chain approximations of reversible jump processes are investigated. Tightness results and a central limit theorem are
established. Moreover, given the generator of a reversible jump process with state space ℝ
d
, the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space H
α/2(ℝ
d
), α∈(0,2), that is equivalent to the standard one.
相似文献
2.
We determine exact values of n-term approximations of q-ellipsoids in the spaces
. 相似文献
3.
《随机分析与应用》2013,31(2):419-441
We consider the stochastic model of water pollution, which mathematically can be written with a stochastic partial differential equation driven by Poisson measure noise. We use a stochastic particle Markov chain method to produce an implementable approximate solution. Our main result is the annealed law of large numbers establishing convergence in probability of our Markov chains to the solution of the stochastic reaction-diffusion equation while considering the Poisson source as a random medium for the Markov chains. 相似文献
4.
In this paper the equation $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}} - \Delta u + a(x)u = |u|^{p - 1} u\;{\rm in }\;{\R}^N $ is considered, when N ≥ 2, p > 1, and $p < {{N + 2} \over {N - 2}}$ if N ≥ 3. Assuming that the potential a(x) is a positive function belonging to $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}L_{{\rm loc}}^{N/2} ({\R}^N )$ such that a(x) → a∞ > 0 as |x|→∞ and satisfies slow decay assumptions but does not need to fulfill any symmetry property, the existence of infinitely many positive solutions, by purely variational methods, is proved. The shape of the solutions is described as is, and furthermore, their asymptotic behavior when $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}|a(x) - a_\infty |_{L_{{\rm loc}}^{N/2} ({\R}^N )} \to 0$ . © 2012 Wiley Periodicals, Inc. 相似文献
5.
6.
该文讨论了一类奇异型随机控制的平稳模型,其费用结构中的函数不限于偶函数,其状态过程为扩散型且具有“非对称的”(关于原点)漂移及扩散系数.因此,奇异型随机控制中的平稳问题被实质性地推广到更一般的形式。该文求得了与此类问题有关的一个变分方程组的解,并且证明了最佳控制的存在性. 相似文献
7.
Paul Andrew 《Mathematische Nachrichten》1994,165(1):183-189
Necessary and sufficient analytical conditions are determined for a singular integral operator of the form aP + bQ with bounded measurable coefficients to be a ?-operator on Lp(Γ) for all 1 < p < ∞. where Γ is a closed Lyapunov curve. 相似文献
8.
Adam Bobrowski 《Annales Henri Poincare》2012,13(6):1501-1510
We show that fast diffusions on finite graphs with semi permeable membranes on vertices may be approximated by finite-state Markov chains provided the related permeability coefficients are appropriately small. The convergence theorem involves a singular perturbation with singularity in both operator and boundary/transmission conditions, and the related semigroups of operators converge in an irregular manner. The result is motivated by recent models of synaptic depression. 相似文献
9.
Robert R. Jensen 《Journal of Fourier Analysis and Applications》1995,2(3):237-259
Let $L[\,\cdot\,]Let
be a nondivergent linear second-order uniformly elliptic partial differential operator defined on functions with domain
Consider the question, "When is a function u a solution of
on
?" The naive answer, "u is a solution of
on
if
and
for all
" is clearly too limited. Indeed, if the coefficients of L are in
then L can be rewritten in divergence form for which the notion of a "weak" solution can be applied. In this case there
could be infinitely many functions that are "weak" but not classical solutions. More importantly, even if the coefficients
of L are just bounded and measurable, the recent results of Krylov permit us to construct "solutions" of
on
and these "solutions" are generally no better than continuous; the "weak" solutions previously mentioned can be obtained
by this construction, too. The preceding discussion provides us with an adequate extrinsic definition of solution (i.e., given
a function u we either prove that it is or is not the result of such a construction) that has been used by several authors,
but one that is not particularly satisfying or illuminating. Our major contribution in this paper is to show the following.
I. There is an intrinsic definition of solution that is equivalent to the extrinsic one. II. Furthermore, the intrinsic definition
is just the (now) well-known Crandall-Lions viscosity solution, modified in a natural way to accommodate measurable coefficients. 相似文献
10.
A new selection principle is proposed for construction of a Feller solution to an ill-posed degenerate diffusion process. This is based on constructing the Feller transition kernel from the unique (under suitable conditions) continuous viscosity solutions to the backward Kolmogorov equation associated with the diffusion. The connection of this Feller process with the small-noise limits of the nondegenerate perturbations of the diffusion and several other related phenomena are also discussed. 相似文献
11.
In this paper, we concern the divergence Kohn-Laplace equation$$\sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {\left( {X_j^*({a^{ij}}{X_i}u) + Y_j^*({b^{ij}}{Y_i}u)} \right)} } + Tu = f - \sum\limits_{i = 1}^n {\left( {X_i^*{f^i} + Y_i^*{g^i}} \right)}$$ with bounded coefficients on the Heisenberg group ${{\mathbb{H}}^n}$, where ${X_1}, \cdots, {X_n},{Y_1}, \cdots, {Y_n}$ and $T$ are real smooth vector fields defined in a bounded region $\Omega \subset {\mathbb{H}^n}$. The local maximum principle of weak solutions to the equation is established. The oscillation properties of the weak solutions are studied and then the Hölder regularity and weak Harnack inequality of the weak solutions are proved. 相似文献
12.
In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain(NSMC) indexed by Cayley tree with any finite states.The asymptotic equipartition properties with almost everywhere(a.e.) convergence for NSMC indexed by Cayley tree are obtained.This article generalizes a recent result. 相似文献
13.
Let (X(t),P
x) and (X(t))},PP}x) be two Hunt processes in duality with respect to an excessive measure and having resolvents that commute. The main result of this article is that if there is an with 0<<1 so that (U
1
U
1
f,f)–U
1
f2 for everyf in 2(), thenX(t) satisfies Hunt's hypothesis (H): every set that is semipolar forX(t) is polar forX(t). 相似文献
14.
15.
Alexander G. Kulakov 《Journal of Approximation Theory》1998,93(3):458-479
Sequences of polynomial functions which converge to solutions of partial differential equations with quasianalytical coefficients are constructed. Estimates of the degree of convergence are also given. 相似文献
16.
Let D be a bounded C~3-domain in R~d and(a_(ij))be a bounded symmetric matrixdefined on D.Consider the symmetric form(u,v)=1/2∫_D a_(ij)(x)(u(x))/(x_i) (v(x))/(x_j)dx,u,v∈H~1(D).Under some assumptions it is shown that the diffusion process associated with the regularDirichlet space(,(H~1(D))on L~2(D)can be characterized as a unique solution of acertain stochastic differential equation. 相似文献
17.
Vassili N. Kolokoltsov 《Applied Mathematics and Optimization》2013,68(1):85-98
The paper is devoted to the well-posedness for nonlinear McKean-Vlasov type diffusions with coefficients depending on the median or, more generally, on the α-quantile of the underlying distribution. The median is not a continuous function on the space of probability measures equipped with the weak convergence. This is one reason why well-posedness of the SDE considered in the paper does not follow by standard arguments. 相似文献
18.
为了研究Markov积分半群的扰动和逼近,根据转移函数与Markov积分半群之间一一对应关系,以及转移函数的扰动和逼近,通过积分的方法,获得了Markov积分半群的广义Phillips扰动定理和Trotter-Kato逼近定理. 相似文献
19.
Arnulf Jentzen 《Potential Analysis》2009,31(4):375-404
We consider the pathwise numerical approximation of nonlinear parabolic stochastic partial differential equations (SPDEs)
driven by additive white noise under local assumptions on the coefficients only. We avoid the standard global Lipschitz assumption
in the literature on the coefficients by first showing convergence under global Lipschitz coefficients but with a strong error
criteria and then by applying a localization technique for one sample path on a bounded set. 相似文献
20.
We obtain necessary and sufficient conditions for the existence and uniqueness of bounded solutions for some classes of linear one- and two-parameter difference equations with operator coefficients in a Banach space. 相似文献