排序方式: 共有27条查询结果,搜索用时 15 毫秒
1.
Kimberly K. J. Kinateder Patrick McDonald 《Proceedings of the American Mathematical Society》1999,127(9):2767-2772
Let be a smoothly bounded domain in Euclidean space and let be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from of a particle driven by where the average is taken over all starting points in
2.
Takaki Hayashi Nakahiro Yoshida 《Annals of the Institute of Statistical Mathematics》2008,60(2):367-406
We consider the problem of estimating the covariance of two diffusion-type processes when they are observed only at discrete
times in a nonsynchronous manner. In our previous work in 2003, we proposed a new estimator which is free of any ‘synchronization’
processing of the original data and showed that it is consistent for the true covariance of the processes as the observation
interval shrinks to zero; Hayashi and Yoshida (Bernoulli, 11, 359–379, 2005). This paper is its sequel. Specifically, it establishes asymptotic normality of the estimator in a general nonsynchronous sampling scheme. 相似文献
3.
We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on Sierpinski gaskets and Sierpinski carpets to their boundaries, where the boundaries are represented by triangles and squares that confine the gaskets and the carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields. These processes behave as an appropriate fractal diffusion within each fractal component of the field. 相似文献
4.
Philip A. Ernst Wilfrid S. Kendall Gareth O. Roberts Jeffrey S. Rosenthal 《Stochastic Processes and their Applications》2019,129(2):355-380
Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts. 相似文献
5.
The truncated variation, TVc, is a fairly new concept introduced in ?ochowski (2008) [5]. Roughly speaking, given a càdlàg function f, its truncated variation is “the total variation which does not pay attention to small changes of f, below some threshold c>0”. The very basic consequence of such approach is that contrary to the total variation, TVc is always finite. This is appealing to the stochastic analysis where so-far large classes of processes, like semimartingales or diffusions, could not be studied with the total variation. Recently in ?ochowski (2011) [6], another characterization of TVc has been found. Namely TVc is the smallest possible total variation of a function which approximates f uniformly with accuracy c/2. Due to these properties we envisage that TVc might be a useful concept both in the theory and applications of stochastic processes. 相似文献
6.
Let X
t be a one-dimensional diffusion of the form dX
t=dB
t+(X
t)dt. Let Tbe a fixed positive number and let
be the diffusion process which is X
t conditioned so that X
0=X
T=x. If the drift is constant, i.e.,
, then the conditioned diffusion process
is a Brownian bridge. In this paper, we show the converse is false. There is a two parameter family of nonlinear drifts with this property. 相似文献
7.
Financial data are often assumed to be generated by diffusions. Using recent results of Fan et al. (J Am Stat Assoc, 102:618–631,
2007; J Financ Econometer, 5:321–357, 2007) and a multiple comparisons procedure created by Benjamini and Hochberg (J R Stat
Soc Ser B, 59:289–300, 1995), we develop a test for non-stationarity of a one-dimensional diffusion based on the time inhomogeneity
of the diffusion function. The procedure uses a single sample path of the diffusion and involves two estimators, one temporal
and one spatial. We first apply the test to simulated data generated from a variety of one-dimensional diffusions. We then
apply our test to interest rate data and real exchange rate data. The application to real exchange rate data is of particular
interest, since a consequence of the law of one price (or the theory of purchasing power parity) is that real exchange rates
should be stationary. With the exception of the GBP/USD real exchange rate, we find evidence that interest rates and real
exchange rates are generally non-stationary. The software used to implement the estimation and testing procedure is available
on demand and we describe its use in the paper. 相似文献
8.
9.
Bruno Bassan Claudia Ceci 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):633-649
We consider optimal stopping problems for Markov processes with a semicontinuous reward function g , and we show that under suitable conditions the value function w = w [ g ] is itself semicontinuous and is a viscosity solution of the associated variational inequality. 相似文献
10.
We describe a Langevin diffusion with a target stationary density with respect to Lebesgue measure, as opposed to the volume measure of a previously-proposed diffusion. The two are sometimes equivalent but in general distinct and lead to different Metropolis-adjusted Langevin algorithms, which we compare. 相似文献