共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper gives a characterization of a Hunt process path by the first exit left limit distribution. It is also showed that if the first exit left limit distribution leaving any ball from the center is a uniform distribution on the sphere, then the Levy Processes are a scaled Brownian motion. 相似文献
2.
本文研究了暂留一致椭圆扩散过程,利用强Markov性,求出了在首中此球之前、末离此球之前和在首中此球与末离此球之间过程的几类极大游程的分布的估计,推广了文献、相关的结果. 相似文献
3.
Several two-boundary problems are solved for a special Lévy process: the Poisson process with an exponential component. The
jumps of this process are controlled by a homogeneous Poisson process, the positive jump size distribution is arbitrary, while
the distribution of the negative jumps is exponential. Closed form expressions are obtained for the integral transforms of
the joint distribution of the first exit time from an interval and the value of the overshoot through boundaries at the first
exit time. Also the joint distribution of the first entry time into the interval and the value of the process at this time
instant are determined in terms of integral transforms. 相似文献
4.
B. P. Harlamov 《Journal of Mathematical Sciences》2002,109(6):2250-2255
The following inverse first exit problem for a Wiener process is considered: to find an upper class with a given distribution of the first exit point from the domain bounded by this curve. Some estimates are obtained for a curve with a given density at zero. Bibliography: 2 titles. 相似文献
5.
《Stochastic Processes and their Applications》2020,130(7):3967-3989
For a spectrally positive strictly stable process with index in (1, 2), we obtain (i) the sub-probability density of its first exit time from an interval by hitting the interval’s lower end before jumping over its upper end, and (ii) the joint distribution of the time, undershoot, and jump of the process when it makes the first exit the other way around. The density of the exit time is expressed in terms of the roots of a Mittag-Leffler function. Some theoretical applications of the results are given. 相似文献
6.
Mathematische Annalen - We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from... 相似文献
7.
This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts–Schmidli model are derived. 相似文献
8.
《Applied Mathematics Letters》2000,13(5):79-83
The detection of HIV-1 levels in human hosts is cast as a first exit time problem for a multidimensional diffusion process. We consider a four-component model for early HIV-1 dynamics including uninfected CD4+ T-cells, latently infected cells, actively infected cells, and HIV-1 virions. An analytical framework is presented for the distribution of the time at which a given virion level is attained. A one-dimensional diffusion approximation for a branching process leads to an estimate for the distribution of the virion density and an expression for the mean detection time for any given detection threshold. 相似文献
9.
Pieper Volkmar Dominé Marco Kurth Petra 《Mathematical Methods of Operations Research》1997,45(3):347-354
Reliability of products is often determined by special technical or physical drift parameters. Suitable stochastic processes are applied to model such drift processes. An failure can be observed when the drift process leaves a given region at the first time. Then the lifetime is the random time to first exit. Applying the first exit theory it is possible to find the type of lifetime distribution. Further the parameters of the lifetime distribution are to be estimated by observations of realisations of the underlying drift process. 相似文献
10.
For a Poisson process with exponentially distributed negative component, we obtain integral transforms of the joint distribution
of the time of the first exit from an interval and the value of the jump over the boundary at exit time and the joint distribution
of the time of the first hit of the interval and the value of the process at this time. On the exponentially distributed time
interval, we obtain distributions of the total sojourn time of the process in the interval, the joint distribution of the
supremum, infimum, and value of the process, the joint distribution of the number of upward and downward crossings of the
interval, and generators of the joint distribution of the number of hits of the interval and the number of jumps over the
interval.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 7, pp. 922–953, July, 2006. 相似文献
11.
Toshiro Watanabe 《Transactions of the American Mathematical Society》2007,359(6):2851-2879
The relation between the upper and lower asymptotic estimates of the density and the fractal dimensions on the sphere of the spectral measure for a multivariate stable distribution is discussed. In particular, the problem and the conjecture on the asymptotic estimates of multivariate stable densities in the work of Pruitt and Taylor in 1969 are solved. The proper asymptotic orders of the stable densities in the case where the spectral measure is absolutely continuous on the sphere, or discrete with the support being a finite set, or a mixture of such cases are obtained. Those results are applied to the moment of the last exit time from a ball and the Spitzer type limit theorem involving capacity for a multi-dimensional transient stable process.
12.
We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary. 相似文献
13.
Pawel Kröger 《Potential Analysis》2018,49(1):203-207
We show that the regularity of a boundary point for a parabolic differential operator in divergence form is under some geometric assumptions equivalent to the property that the density of the exit distribution for a time reversed process vanishes at that point. We give regularity and irregularity criterions for equations with variable coefficients. Thus, the known result on the Fulks measure that states that the density with respect to the Lebesgue measure vanishes at the point opposite to the center of the heat ball (see Fulks (Proc. Am. Math. Soc. 17, 6–11 1966)) can be extended to exit distributions for more general regions and parabolic differential operators. 相似文献
14.
15.
Given a compact symmetric space, M, we obtain the mean exit time function from a principal orbit, for a Brownian particle starting and moving in a generalized ball whose boundary is the principal orbit. We also obtain the mean exit time flmction of a tube of radius r around special totally geodesic submanifolds P of M. Finally we give a comparison result for the mean exit time function of tubes around submanifolds in Riemannian manifolds, using these totally geodesic submanifolds in compact symmetric spaces as a model. 相似文献
16.
We study exit times from a set for a family of multivariate autoregressive processes with normally distributed noise. By using the large deviation principle, and other methods, we show that the asymptotic behavior of the exit time depends only on the set itself and on the covariance matrix of the stationary distribution of the process. The results are extended to exit times from intervals for the univariate autoregressive process of order n, where the exit time is of the same order of magnitude as the exponential of the inverse of the variance of the stationary distribution. 相似文献
17.
We present a multiscale analysis for the exit measures from large balls in , of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment corresponding
to simple random walk. Our main assumption is an isotropy assumption on the law of the environment, introduced by Bricmont
and Kupiainen. Under this assumption, we prove that the exit measure of the random walk in a random environment from a large
ball, approaches the exit measure of a simple random walk from the same ball, in the sense that the variational distance between
smoothed versions of these measures converges to zero. We also prove the transience of the random walk in random environment.
The analysis is based on propagating estimates on the variational distance between the exit measure of the random walk in
random environment and that of simple random walk, in addition to estimates on the variational distance between smoothed versions
of these quantities.
Partially supported by NSF grant DMS-0503775. 相似文献
18.
We study the distribution of the exit place of iterated Brownian motion in a cone, obtaining information about the chance of the exit place having large magnitude. Along the way, we determine the joint distribution of the exit time and exit place of Brownian motion in a cone. This yields information on large values of the exit place (harmonic measure) for Brownian motion. The harmonic measure for cones has been studied by many authors for many years. Our results are sharper than any previously obtained. 相似文献
19.
Philip S. Griffin 《Journal of Theoretical Probability》2010,23(4):1092-1109
Pruitt’s estimates on the expectation and the distribution of the time taken by a random walk to exit a ball of radius r are extended to the infinite-dimensional setting. It is shown that they separate into two pairs of estimates depending on
whether the space is type 2 or cotype 2. It is further shown that these estimates characterize type 2 and cotype 2 spaces. 相似文献
20.
B. P. Harlamov 《Journal of Mathematical Sciences》2005,128(1):2625-2639
Semi-Markov processes of diffusion type in the d-dimensional space (d > 1) are considered. We assume that the transition generating function of such a process satisfies a second-order differential equation of elliptic type. We apply methods of differential equations theory, especially of the theory of the Dirichlet problem, to study the transition generating function for a small neighborhood of the initial point of the process. Asymptotic expansions in the small scale parameter are obtained both for the first exit point distribution density and for the first exit time expectation for the case where the trajectory of the process leaves a small neighborhood of the initial point. We prove the existence of the Dynkin characteristic operator determined by a decreasing sequence of neighborhoods. Bibliography: 9 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 293, 2003, pp. 226–251. 相似文献