Showing papers in "Stochastic Processes and their Applications in 1983"

TL;DR: In this article, it was shown that the model is complete if and only if there exists a unique martingale measure, i.e., the model can be represented as a stochastic integral with respect to the discounted price process.

TL;DR: In this article, sufficient conditions for a renewal measure to be of order o(ψ(n)-1) were derived, where π is the invariant probability measure, λ an initial distribution and ψ belongs to a suitable class of nondecreasing sequences.

TL;DR: In this paper, a generalized version of the Ferguson-Klass construction with uniform convergence was proposed for centred sums of independent random variables, and an analogue of the Levy-Ito decomposition for Levy processes was developed, which enables a number of simple sample function properties of these processes to be read off from the Levy measure in their characteristic functionals.

TL;DR: In this paper, it was shown that the conditional density of the present state, given the past observations, is a mixture of Gaussian distributions, and is parametrically determined by two sets of sufficient statistics which satisfy stochastic DEs.

TL;DR: In this article, conditions of tightness for sequences of processes are studied, which are mostly based on the use of dominating increasing processes. But they are not applicable to processes that are not quasi-left-continuous.

TL;DR: In this article, a chaine de Markov homogene { X n } is considered, and the densite de the probabilite de transition is estimated by l'aide d'estimateurs a noyaux.

TL;DR: The limit theorems for Lt(u) and P (M(t) > u) for u→∞ are obtained under the hypothesis that the distribution of the random norm (Σkj=0(U2j+V2j))1 2 belongs to the domain of attraction of the extreme value distribution exp{ e−2} as discussed by the authors.

TL;DR: In this article, it was shown that goodness-of-fit tests based on these statistics are asymptotically sensitive only in the extreme tails of a distribution, which is exactly where such statistics that use a weight function w v with 1 2 ⩽ v 1 2 are insensitive.

TL;DR: In this article, the strictly stationary random sequences satisfying "absolute regularity" were constructed, which is a 0−1 instantaneous function of an aperiodic Markov chain with countable irreducible state space, such that n−2 var (X1 + ⋯ + Xn) approaches 0 arbitrarily slowly as n → ∞ and (X 1 + ε+ε+Xn) is partially attracted to every divisible law.

TL;DR: The central limit theorem for estimates of parameters which specify the covariance structure of a zero mean, stationary, Gaussian, discrete time series observed at unequally spaced times was proved in this paper.

TL;DR: In this article, the authors studied the convergence of point processes and random measures on the real line that satisfy a weak law of large numbers, showing that the thinning process (normalized by a certain function) converges in distribution if and only if the thinening process does.

TL;DR: In this paper, the authors obtained several almost sure and L p convergence properties of generalized linear processes and showed that these convergence properties are related to certain second order properties of the process.

TL;DR: The limit distribution of the lengths of increasing runs is studied in this paper, where a strong theorem is given to characterize the limit behavior of the longest increasing block in a sequence of independent, uniform (0, 1) r.v.'s.

TL;DR: In this article, it was shown that the maximum likelihood estimator is efficient in the sense of having asymptotically maximum probability of concentration about the true parameter value, under mild regularity conditions on the random information matrix.

TL;DR: In this paper, the Neyman's C (α) type test is shown to be not efficient for nonergodic stochastic processes and the likelihood-ratio statistic is not fully efficient for the model discussed in this paper.

TL;DR: In this paper, a class of two-parameter processes which are diffusions on each coordinate and satisfy a particular Markov property related to the partial ordering in R 2 + is introduced.

TL;DR: In this paper, nonlinear filtering equations for two-parameter semimartingales of a Brownian sheet are obtained by an extended reference probability method, also applicable to the known Gaussian linear models.

TL;DR: In this article, a general model involving k competing risks is studied and the hazard rates of these risks are simultaneously estimated by Gaussian processes and the limiting distribution of certain statistics are obtained.

TL;DR: In this article, the existence of an integer-valued function n = n(m), tϵ[0, 1], and centering constants bms, 0⩽s ⩽ m, such that Z (m) (t)= √ ∑ s=0 m b ms converges to the Brownian bridge process in terms of its finite-dimensional distributions.

TL;DR: In this paper, a non-linear estimator for the ergodic Gauss-Markov process with mean zero and covariance function e −|τ| was proposed.

TL;DR: In this paper, the authors studied the problem of existence of jointly continuous local time for two-parameter Levy processes and proved that if X is R -valued and its lower index is greater than one, then a jointly continuous (at least outside {(x,s,t): x = 0}) local time can be obtained via Berman's method.

TL;DR: In this paper, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation, and no criterion can be defined for non-stationary stochastic processes.

TL;DR: In this article, the authors studied the asymptotic behavior of the particle numbers in bounded domains of a binary splitting one-dimensional branching diffusion process and gave a Yaglom type limit theorem in the so-called locally subcritical case, and almost sure convergence of the normalized particle number in the locally supercritical case.

TL;DR: In this article, the transport of solid particles in a turbulent fluid flowing through a tank is approximated by one-dimensional random walks in both discrete and continuous time, and general formulae are derived for the probabilities of sedimentation and exit of the particles, and detailed results obtained for the case where their movement is strictly nonnegative.

TL;DR: In this paper, a necessary and sufficient condition for the existence of a non-degenerate limit with expectation norming was given and it was shown that if the limit is not degenerate, its expectation must be equal to 1.

TL;DR: In this article, the authors considered necessary and sufficient conditions for the Markov property on sets B, C: F (B), F (C) c. This implies a necessary condition proved by Dynkin in a recent preprint for the case where B∪C=E and B,C are finely closed.

TL;DR: In this paper, a random measure whose distribution depends on NA is introduced, from which exact estimates and a recursive method for updating them are obtained as further observations become available, for estimation of an unknown, random scalar multiplier of a known measure, of a symmetrically distributed directing measure M and of a Markov-directed Cox process on R.

TL;DR: In this article, a general invariance principle for empirical processes indexed by smooth functions was derived and applied to prove bounds for the convergence of the empirical distributions which might be useful to verify asymptotic normality of smooth statistical functionals.

TL;DR: A formula for the expectation of the (d − 1)-dimensional measure of the intersection of a Gaussian stationary random field with a fixed level u is given in this paper, where the expectation is based on the expectation for the ( d − 1) dimension of the random field.

TL;DR: In this article, the theory of stochastic integration w.r.t. continuous local martingales using a simple time change technique was developed, allowing progressively measurable integrands.