共查询到20条相似文献,搜索用时 265 毫秒
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By making full use of heat kernel estimates, we establish the integral tests on the zero-one laws of upper and lower bounds for the sample path ranges of symmetric Markov processes. In particular, these results concerning on upper rate bounds are applicable for local and non-local Dirichlet forms, while lower rate bounds are investigated in both subcritical setting and critical setting. 相似文献
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A coupling method is used to obtain the explicit upper and lower bounds for convergence rates in strong ergodicity for Markov processes. For one-dimensional diffusion processes and birth–death processes, these bounds are sharp in the sense that the upper one and the lower one only differ in a constant. 相似文献
4.
Jian Wang 《数学学报(英文版)》2012,28(10):1995-2010
By adopting a nice auxiliary transform of Markov operators, we derive new bounds for the first eigenvalue of the generator corresponding to symmetric Markov processes. Our results not only extend the related topic in the literature, but also are efficiently used to study the first eigenvalue of birth-death processes with killing and that of elliptic operators with killing on half line. In particular, we obtain two approximation procedures for the first eigenvalue of birth-death processes with killing, and present qualitatively sharp upper and lower bounds for the first eigenvalue of elliptic operators with killing on half line. 相似文献
5.
Andrew M. Ross 《Methodology and Computing in Applied Probability》2010,12(1):111-138
We compute upper and lower bounds on the expected maximum of correlated normal variables (up to a few hundred in number) with
arbitrary means, variances, and correlations. Two types of bounding processes are used: perfectly dependent normal variables,
and independent normal variables, both with arbitrary mean values. The expected maximum for the perfectly dependent variables
can be evaluated in closed form; for the independent variables, a single numerical integration is required. Higher moments
are also available. We use mathematical programming to find parameters for the processes, so they will give bounds on the
expected maximum, rather than approximations of unknown accuracy. Our original application is to the maximum number of people
on-line simultaneously during the day in an infinite-server queue with a time-varying arrival rate. The upper and lower bounds
are tighter than previous bounds, and in many of our examples are within 5% or 10% of each other. We also demonstrate the
bounds’ performance on some PERT models, AR/MA time series, Brownian motion, and product-form correlation matrices. 相似文献
6.
We give equivalent characterizations for off-diagonal upper bounds of the heat kernel of a regular Dirichlet form on the metric
measure space, in two settings: for the upper bounds with the polynomial tail (typical for jump processes) and for the upper
bounds with the exponential tail (for diffusions). Our proofs are purely analytic and do not use the associated Hunt process. 相似文献
7.
As many numerical processes for time discretization of evolution equations can be formulated as analytic mappings of the generator, they can be represented in terms of the resolvent. To obtain stability estimates for time discretizations, one therefore would like to carry known estimates on the resolvent back to the time domain. For different types of bounds of the resolvent of a linear operator, bounds for the norm of the powers of the operator and for their sum are given. Under similar bounds for the resolvent of the generator, some new stability bounds for one-step and multistep discretizations of evolution equations are then obtained. 相似文献
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《Mathematical and Computer Modelling》2000,31(10-12):129-142
When viewed at an appropriate scale, a disordered medium can behave as if it is strictly less than three-dimensional. As fractals typically have noninteger dimensions, they are natural models for disordered media, and diffusion on fractals can be used to model transport in disordered media. In particular, such diffusion processes can be used to obtain bounds on the fundemantal solution to the heat equation on a fractal. In this paper, we review the work in this area and describe how bounds on branching processes lead to bounds on heat kernels. 相似文献
9.
Yong-hua Mao 《Frontiers of Mathematics in China》2006,1(1):105-109
Coupling method is used to obtain the explicit upper and lower bounds for convergence rates in strong ergodicity for Markov
processes. For one-dimensional diffusion processes and birth-death processes, these bounds are sharp in the sense that the
upper one and the lower one are only different by a constant.
This announcement is an outline of an original research paper “Convergence Rates in Strong Ergodicity for Markov Processes”
that will appear in Stoch. Process. Their Appl. 相似文献
10.
《Journal of Computational and Applied Mathematics》1998,89(2):257-261
For the numerical evaluation of finite-part integrals with singularities of order p ⩾ 1, we give error bounds for quadrature methods based on spline approximation. These bounds behave in the same way as the optimal ones. The ideas of the proof are also useful for methods based on other approximation processes. 相似文献
11.
Bruce Hajek 《Probability Theory and Related Fields》1985,68(3):315-329
Summary Stochastic bounds are derived for one dimensional diffusions (and somewhat more general random processes) by dominating one process pathwise by a convex combination of other processes. The method permits comparison of diffusions with different diffusion coefficients. One interpretation of the bounds is that an optimal control is identified for certain diffusions with controlled drift and diffusion coefficients, when the reward function is convex. An example is given to show how the bounds and the Liapunov function technique can be applied to yield bounds for multidimensional diffusions.This work was supported by the Office of Naval Research under Contract N00014-82-K-0359 and the U.S. Army Research Office under Contract DAAG29-82-K-0091 (administered through the University of California at Berkeley). 相似文献
12.
Di Xin ZHANG 《数学学报(英文版)》2006,22(2):339-346
So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions. 相似文献
13.
In this paper we present a probabilistic approach for the estimation of realistic error bounds appearing in the execution of basic algebraic floating point operations. Experimental results are carried out for the extended product, the extended sum, the inner product of random normalised numbers, the product of random normalised matrices and the solution of lower triangular systems The ordinary and probabilistic bounds are calculated for all the above processes and generally in all the executed examples the probabilistic bounds are much more realistic. 相似文献
14.
We investigate Hoeffding's inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the inequalities are obtained via the solution of Poisson's equation. The results are further illustrated with applications to queueing theory and reective diffusion processes. 相似文献
15.
《Stochastic Processes and their Applications》1987,24(1):51-60
The well-known submartingale maximal inquality of Birnbaum and Marshall (1961) is generalized to provide upper tail inequalities for suprema of processes which are products of a submartingale by a nonincreasing nonnegative predictable process. The new inequalities are proved by applying an inequality of Lenglart (1977), and are then used to provide best-possible universal growth-rates for a general submartingale in terms of the predictable compensator of its positive part. Applications of these growth rates include strong asymptotic upper bounds on solutions to certain stochastic differential equations, and strong asymptotic lower bounds on Brownian-motion occupation-times. 相似文献
16.
In this paper we study the transition densities for a large class of non-symmetric Markov processes whose jumping kernels decay exponentially or subexponentially. We obtain their upper bounds which also decay at the same rate as their jumping kernels. When the lower bounds of jumping kernels satisfy the weak upper scaling condition at zero, we also establish lower bounds for the transition densities, which are sharp. 相似文献
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In this paper we derive general upper bounds for the total variation distance between the distributions of a partial sum process in row-wise independent, non-negative triangular arrays and the sum of a fixed number of corresponding extremal processes. As a special case we receive bounds for the supremum distance between the distribution functions of a partial sum and the sum of corresponding upper extremes which improve upon existing results. The outcome may be interpreted as the influence of large insurance claims on the total loss. Moreover, under an additional infinitesimal condition we also prove explicit bounds for limits of the above quantities. Thereby we give a didactic and elementary proof of the Ferguson–Klass representation of Lévy processes on ??≥?0 which reflects the influence of extremal processes in insurance. 相似文献
18.
Thomas Wanner 《Transactions of the American Mathematical Society》2004,356(6):2251-2279
Many interesting and complicated patterns in the applied sciences are formed through transient pattern formation processes. In this paper we concentrate on the phenomenon of spinodal decomposition in metal alloys as described by the Cahn-Hilliard equation. This model depends on a small parameter, and one is generally interested in establishing sharp lower bounds on the amplitudes of the patterns as the parameter approaches zero. Recent results on spinodal decomposition have produced such lower bounds. Unfortunately, for higher-dimensional base domains these bounds are orders of magnitude smaller than what one would expect from simulations and experiments. The bounds exhibit a dependence on the dimension of the domain, which from a theoretical point of view seemed unavoidable, but which could not be observed in practice.
In this paper we resolve this apparent paradox. By employing probabilistic methods, we can improve the lower bounds for certain domains and remove the dimension dependence. We thereby obtain optimal results which close the gap between analytical methods and numerical observations, and provide more insight into the nature of the decomposition process. We also indicate how our results can be adapted to other situations.
19.
《Journal of Complexity》2004,20(1):108-131
We study minimal errors and optimal designs for weighted L2-approximation and weighted integration of Gaussian stochastic processes X defined on the half-line [0,∞). Under some regularity conditions, we obtain sharp bounds for the minimal errors for approximation and upper bounds for the minimal errors for integration. The upper bounds are proven constructively for approximation and non-constructively for integration. For integration of the r-fold integrated Brownian motion, the upper bound is proven constructively and we have a matching lower bound. 相似文献
20.
The paper deals with non asymptotic computable bounds for the geometric convergence rate of homogeneous ergodic Markov processes. Some sufficient conditions are stated for simultaneous geometric ergodicity of Markov chain classes. This property is applied to nonparametric estimation in ergodic diffusion processes. 相似文献