共查询到20条相似文献,搜索用时 31 毫秒
1.
Tobias Rydén D. M. Titterington 《Journal of computational and graphical statistics》2013,22(2):194-211
Abstract Versions of the Gibbs Sampler are derived for the analysis of data from hidden Markov chains and hidden Markov random fields. The principal new development is to use the pseudolikelihood function associated with the underlying Markov process in place of the likelihood, which is intractable in the case of a Markov random field, in the simulation step for the parameters in the Markov process. Theoretical aspects are discussed and a numerical study is reported. 相似文献
2.
Abstract In this paper we study strongly continuous positive semigroups on particular classes of weighted continuous function space
on a locally compact Hausdorff space X having a countable base.
In particular we characterize those positive semigroups which are the transition semigroups of suitable Markov processes.
Some applications are also discussed.
Keywords Positive semigroup, Markov transition function, Markov process, Weighted continuous function space, Degenerate second order
differential operator
Mathematics Subject Classification (2000) 47D06, 47D07, 60J60 相似文献
3.
Robert J. Elliott 《随机分析与应用》2013,31(6):1165-1177
Abstract In this paper, we use filtering techniques to estimate the occurrence time of an event in a financial market. The occurrence time is being viewed as a Markov stopping time with respect to the σ-field generated by a hidden Markov process. We also generalize our result to the Nth occurrence time of that event. 相似文献
4.
Daniel Egloff 《Applied Mathematical Finance》2013,20(3):287-305
Abstract This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. Following the ideas of Menaldi et al., we transform the constrained into an unconstrained optimal stopping problem. The transformation replaces the original payoff by the value of a generalized barrier option. We also provide a Monte Carlo method to numerically calculate the option value for multidimensional Markov processes. We adapt the Longstaff–Schwartz algorithm to solve the stochastic Cauchy–Dirichlet problem related to the valuation problem of the barrier option along a set of simulated trajectories of the underlying Markov process. 相似文献
5.
《随机分析与应用》2013,31(6):1283-1303
Abstract The evolution of a biological system, like a cellular one, is analyzed by constructing a Markov process on a suitable state space. This is performed by the introduction of an infinitesimal generator for the Markov semigroup associated to this process. A measure valued process is then defined in a natural way and it is proved that his first moment satisfies the Sharpe–Lotka system in a distributional sense. Hence the study of the moments of the process is tried. An involved integral equation for the moment generating functional is derived. 相似文献
6.
We extend the central limit theorem for additive functionals of a stationary, ergodic Markov chain with normal transition operator due to Gordin and Lif?ic, 1981 [A remark about a Markov process with normal transition operator, In: Third Vilnius Conference on Probability and Statistics 1, pp. 147–48] to continuous-time Markov processes with normal generators. As examples, we discuss random walks on compact commutative hypergroups as well as certain random walks on non-commutative, compact groups. 相似文献
7.
Steven L. Scott 《Journal of computational and graphical statistics》2013,22(3):662-670
Abstract We postulate observations from a Poisson process whose rate parameter modulates between two values determined by an unobserved Markov chain. The theory switches from continuous to discrete time by considering the intervals between observations as a sequence of dependent random variables. A result from hidden Markov models allows us to sample from the posterior distribution of the model parameters given the observed event times using a Gibbs sampler with only two steps per iteration. 相似文献
8.
ABSTRACTThe asymptotic equipartition property is a basic theorem in information theory. In this paper, we study the strong law of large numbers of Markov chains in single-infinite Markovian environment on countable state space. As corollary, we obtain the strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for this process. Finally, we give the asymptotic equipartition property of Markov chains in single-infinite Markovian environment on countable state space. 相似文献
9.
《随机分析与应用》2013,31(6):1207-1214
Abstract In this article, we assume that we have a number of candidate insurance models for describing a risk process. Suppose that in each model the risk process is a function of the states of some Markov chains. Based on observing the history of the premiums and claims processes we propose dynamics whose solutions indicate the likelihoods of each candidate model. 相似文献
10.
This paper concerns the filtering of an R
d
-valued Markov pure jump process when only the total number of jumps are observed. Strong and weak uniqueness for the solutions
of the filtering equations are discussed.
Accepted 12 November 1999 相似文献
11.
Zoran Vondraček 《Probability Theory and Related Fields》1995,101(3):393-407
Summary LetD be a bounded domain inR
d
with regular boundary. LetX=(Xt, Px) be a standard Markov process inD with continuous paths up to its lifetime. IfX satisfies some weak conditions, then it is possible to add a non-local part to its generator, and construct the corresponding standard Markov process inD with Brownian exit distributions fromD.This work was done while the author was an Alexander von Humboldt fellow at the Universität des Saarlandes in Saarbrücken, Germany 相似文献
12.
Alexandre Bureau James P. Hughes Stephen C. Shiboski 《Journal of computational and graphical statistics》2013,22(4):621-632
Abstract Hidden Markov models (HMM) can be applied to the study of time varying unobserved categorical variables for which only indirect measurements are available. An S-Plus module to fit HMMs in continuous time to this type of longitudinal data is presented. Covariates affecting the transition intensities of the hidden Markov process or the conditional distribution of the measured response (given the hidden states of the process) are handled under a generalized regression framework. Users can provide C subroutines specifying the parameterization of the model to adapt the software to a wide variety of data types. HMM analysis using the S-Plus module is illustrated on a dataset from a prospective study of human papillomavirus infection in young women and on simulated data. 相似文献
13.
AbstractIn this paper, we develop an option valuation model where the dynamics of the spot foreign exchange rate is governed by a two-factor Markov-modulated jump-diffusion process. The short-term fluctuation of stochastic volatility is driven by a Cox–Ingersoll–Ross (CIR) process and the long-term variation of stochastic volatility is driven by a continuous-time Markov chain which can be interpreted as economy states. Rare events are governed by a compound Poisson process with log-normal jump amplitude and stochastic jump intensity is modulated by a common continuous-time Markov chain. Since the market is incomplete under regime-switching assumptions, we determine a risk-neutral martingale measure via the Esscher transform and then give a pricing formula of currency options. Numerical results are presented for investigating the impact of the long-term volatility and the annual jump intensity on option prices. 相似文献
14.
Nicolas Privault Wim Schoutens 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):289-316
We show that for the binomial process (or Bernoulli random walk) the orthogonal functionals constructed in Kroeker, J.P. (1980) "Wiener analysis of functionals of a Markov chain: application to neural transformations of random signals", Biol. Cybernetics 36 , 243-248, [14] for Markov chains can be expressed using the Krawtchouk polynomials, and by iterated stochastic integrals. This allows to construct a chaotic calculus based on gradient and divergence operators and structure equations, and to establish a Clark representation formula. As an application we obtain simple infinite dimensional proofs of covariance identities on the discrete cube. 相似文献
15.
Estimation in Stationary Markov Renewal Processes,with Application to Earthquake Forecasting in Turkey 总被引:1,自引:0,他引:1
Consider a process in which different events occur, with random inter-occurrence times. In Markov renewal processes as well as in semi-Markov processes, the sequence of events is a Markov chain and the waiting distributions depend only on the types of the last and the next event. Suppose that the state-space is finite and that the process started far in the past, achieving stationary. Weibull distributions are proposed for the waiting times and their parameters are estimated jointly with the transition probabilities through maximum likelihood, when one or several realizations of the process are observed over finite windows. The model is illustrated with data of earthquakes of three types of severity that occurred in Turkey during the 20th century.AMS 2000 Subject Classification: 60K20 相似文献
16.
Kangkang Wang 《随机分析与应用》2013,31(6):1117-1128
Abstract In this article, a class of strong limit theorems for relative entropy density of arbitrary stochastic sequence, expressed by inequalities, are obtained by comparing arbitrary dependent distribution with and the mth-order Markov distribution on probability space. As corollaries, some Shannon–McMillan theorems of mth-order nonhomogeneous Markov information source are obtained. Some results of nonhomogeneous Markov information source obtained are generalized. 相似文献
17.
Abstract This article is concerned with studying the following problem: Consider a multivariate stochastic process whose law is characterized in terms of some infinitesimal characteristics, such as the infinitesimal generator in case of finite Markov chains. Under what conditions imposed on these infinitesimal characteristics of this multivariate process, the univariate components of the process agree in law with given univariate stochastic processes. Thus, in a sense, we study a stochastic processe' counterpart of the stochastic dependence problem, which in case of real valued random variables is solved in terms of Sklar's theorem. 相似文献
18.
Abstract We provide in this paper a systematic development of nonlinear stochastic difference equations driven by martingales (that depend on a spatial parameter); three such equations are considered. We begin with the existence and uniqueness of solutions and continue with the study of stochastic properties, such as the martingale and Markov properties, along with ? irreducibility and recurrence. We discuss in the final section the discrete-time flow and asymptotic flow properties of the solution process. 相似文献
19.
Mina Ossiander 《Probability Theory and Related Fields》2005,133(2):267-298
A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in R3 with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations of functionals of a Markov process indexed by the nodes of a binary tree. It gives existence and uniqueness of weak solutions for all time under relatively simple conditions on the forcing and initial data. These conditions involve comparison of the forcing and initial data with majorizing kernels. 相似文献
20.
Hans G. Kellerer 《Probability Theory and Related Fields》1987,76(1):71-80
Summary A point process
on R
+ can be represented by the associated counting process (ξ
t
;t∈
R
+) or by the associated sequence of jump times (τ
n
;n∈
Z
+) and in accordance may possess two types of Markov property. The present paper first clarifies their mutual dependence, leading
in particular to the notion of “weak multiplicativity” for the joint distribution of two consecutive jump times. Then, by
means of results from a previous paper, a uniquely determined “Markov variant”
is assigned to
without changing the one-dimensional marginals. This provides in particular a new characterization of the Poisson process
by these marginals and the adequate Markov property. Further applications concern the explicit construction of the compensator
and certain transition probabilities of
. 相似文献