Nonlinear Filtering for Diffusions in Random Environments

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X ^W and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition.     

Stochastic analysis in life office management: applications to large annuity portfolios

The paper deals with the riskiness analysis for a large portfolio of life annuities. By means of the limiting distribution of the present value of the portfolio, in the first part of the paper a model for evaluating the investment and the projection risks is presented. In the second part, with regard to the investment risk's effects, the insolvency risk is measured considering the cumulative probability distribution function of the discounted average cost per policy. Copyright © 2003 John Wiley & Sons, Ltd.     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

Some Results for the Compound Poisson Process That Is Perturbed by Diffusion

Abstract In the present paper surplus process perturbed by diffusion are considered.The distributions ofthe surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation andruin caused by a claim are studied.Some joint distribution densities are obtained.Techniques from martingaletheory and renewal theory are used.     

分布变点模型的非参数检验和区间估计

提 要设　是定义在［０,１］上的随机过程Ｘ（ｔ）的ｎ个等距独立观察值,其中,　服从公共连续分布Ｆ;,服从公共连续分布 Ｆ＊,Ｆ与Ｆ＊不同;其中,是过程 Ｘ（ｔ）的变点．用ＣＵＳＵＭ及Ｂｒｏｗｎｉａｎ Ｓｈｅｅｔ方法给出了检测变点τ位置的一个程序,并证明了所得结果是强相合的;同时也讨论了τ的假设检验和区间估计．     

Asymptotically minimax testing ofr>2 simple hypotheses

In this paper, we consider the problem of asymptotically minimax testing ofr≥2 simple hypotheses when a general stochastic process is observed. We establish general conditions for the exponential decrease of maximal probability errors of minimax tests as the number of observations increases. At the present time, similar results for testing several multinomial schemes were obtained by Salihov [8]. Similar results for testing two simple hypotheses were obtained in [5]. In the proofs of the main results, we use the theory of large deviations ([3], [2]). In Sec. 1, the main result is proved. In Secs. 2–4, we analyze the i.i.d. case, nonhomogeneous Poisson processes, and renewal processes as examples. Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 313–320, July–September, 2000.     

关于非负下半连续函数最优可测耦合的存在性及其应用

本文证明了两个转移概率关于非负下半连续函数最优可测耦合的存在性定理．作为对这一结果的应用,推广了Ｓｔｒａｓｓｅｎ定理,进而证明了跳过程的随机可比性等价于保序耦合的存在性．     

Effect of Conversion Process([I]-P→ΛΛ) in[I]--Hypernuclei

Effect of conversion process ([I]-P→ΛΛ) on[I]--hypernucleus is studied for [I]12-Be. It is found that theconversion process has a certain extent effect on properties of low-lying states of the[I]--hypernuclei.     

A generalization of inverse distance weighting and an equivalence relationship to noise-free Gaussian process interpolation via Riesz representation theorem

In this paper, we show the relationship between two seemingly unrelated approximation techniques. On the one hand, a certain class of Gaussian process-based interpolation methods, and on the other hand inverse distance weighting, which has been developed in the context of spatial analysis where there is often a need for interpolating from irregularly spaced data to produce a continuous surface. We develop a generalization of inverse distance weighting and show that it is equivalent to the approximation provided by the class of Gaussian process-based interpolation methods. The equivalence is established via an elegant application of Riesz representation theorem concerning the dual of a Hilbert space. It is thus demonstrated how a classical theorem in linear algebra connects two disparate domains.     

Convex integral functionals of regular processes

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be identified with the space of optional random measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for a systematic treatment of stochastic optimization problems over BV processes and, in particular, yields a maximum principle for a general class of singular stochastic control problems.