Showing papers in "Stochastic Processes and their Applications in 1995"

TL;DR: In this paper, the existence and uniqueness of the adapted solution to a backward stochastic differential equation under a weaker condition than the Lipschitz one was established, and a new theorem was established.

TL;DR: A general model for an epidemic in a closed, homogeneously mixing population is presented in this paper, where a construction of a sequence of such epidemics, indexed by the initial number of susceptibles N from the limiting branching process is described.

TL;DR: In this paper, a mapping I : D[0, ∞)×D[ 0,∞)→D[0 ∞] is constructed such that if (Xt) is a semimartingale on a probability space (Ω, F, P) with respect to a filtration (F t) and if (ft) is an r.c.l.s. ( F t) adapted process, then I (ƒ, X. (ω))= ∫ 0. ƒ−dX(ω

TL;DR: This article developed the theory of fractionally differenced ARIMA time series with stable infinite variance innovations establishing conditions for existence and invertibility, and analyzed their asymptotic dependence structure by means of the codifference and the covariation measures of dependence which are extensions of the covariance and are applicable to stochastic processes with infinite variance.

TL;DR: In this paper, the problem of maximizing the expected total utility from consumption and the expected utility from terminal wealth is addressed, where the price process of the available financial assets is assumed to satisfy a system of functional stochastic differential equations, and the consumption and investment processes are adapted to the natural filtration of the price processes.

TL;DR: In this paper, the authors define a covariation process [X, Y] with the help of a limit procedure, where X and Y are two general stochastic processess.

TL;DR: The noisy voter model is a spin system on a graph which may be obtained from the basic voter model by adding spontaneous flipping from 0 to 1 and from 1 to 0 at each site as mentioned in this paper.

TL;DR: In this article, the authors show that for up-and-down pulses with random moments of birth τ and random lifetime w determined by a Poisson random measure, when the pulse amplitude e → 0, while the pulse density δ increases to infinity, one obtains a process of fractal sum of micropulses.

TL;DR: In this article, a class of linear stochastic differential equations in Hilbert spaces is studied, which allows to construct probability densities and to generate changes in the probability measure one started with.

TL;DR: In this paper, the authors considered nonhomogeneous birth and death processes and obtained upper and lower bounds on the rate of convergence of these processes, and studied the convergence rate of birth-death processes on a finite state space.

TL;DR: The large deviation principle is known to hold for the empirical measures (occupation times) of Polish space valued random variables under Markov dependence or mixing conditions, and subject to the appropriate exponential tail conditions as discussed by the authors.

TL;DR: In this paper, it was shown that the degree of smoothness of α ( x ) in terms of eventually negative order Sobolev spaces with respect to the canonical Dirichlet structure on Wiener space can be obtained by renormalizing α( x ) as | x | → 0.

TL;DR: The random-cluster measures converge weakly to the uniform spanning tree measure of Pemantle (1991) as p, q --> 0 in such a way that q/p --> 0.

TL;DR: In this article, a solution to a stochastic partial differential equation (in the Stratonovitch form) is an almost sure limit of solutions to a sequence of approximated equations (with Brownian path w ( t ) being replaced by a piecewise smooth path w n ( t ), approximating w( t )).

TL;DR: In this article, a semilinear stochastic equation in a real Hilbert space and a related McKean-Vlasov type measure-valued evolution equation are discussed.

TL;DR: The law of the iterated logarithm for U -processes indexed by canonical Vapnik-Cervonenkis classes of functions with square integrable envelope was proved in this paper.

TL;DR: In this paper, an implicit approximation scheme for the heat equation with a nonlinear term and an additive space-time white noise was proposed, which converges to the unique solution in probability, uniformly in space and time.

TL;DR: For a given functional of a simple point process, an analogue of Taylor's theorem for its mean value was found in this paper, where the terms of the expansion are integrals of some real functions with respect to factorial moment measures of the point process.

TL;DR: In this article, the authors consider convergence of a recursive projection scheme for a stochastic differential equation reflecting on the boundary of a convex domain G. If G satisfies Condition (B) in Tanaka (1979), they obtain mean square convergence, pointwise, with the rate O ((δ log 1 δ ) 1 2 ), and if G is a convexonymetric polyhedron, they also give a convergence rate of O( √ √ log 1 ǫ ) on compacts.

TL;DR: In this paper, an upper and a lower bound of large deviations from the hydrodynamical limit of the empirical measure for a class of zero range processes in infinite volume starting from equilibrium was proved.

TL;DR: A uniform bound for estimating the moving-average coefficients via autoregressive approximation being uniform over all integers is given.

TL;DR: In this paper, the authors apply the blockwise bootstrap for stationary observations, proposed by Kunsch (1989), to empirical processes indexed by function classes F which satisfy some bracketing conditions.

TL;DR: In this paper, the authors considered the effects of adding an asymptotically small random perturbation to a planar dynamical system with a saddle point equilibrium and obtained a new limit law for the exit time from a neighborhood of the saddle, assuming the initial point is on the stable manifold.

TL;DR: In this paper, a discrete version of the in-law problem is formulated in which ordinary multiplication is replaced by a lattice-preserving operation whose definition involves a subcritical Markov branching process and it is shown that the existence, uniqueness and representation theory for the continuous problem transfers to the discrete problem.

TL;DR: It is proved that, under suitable conditions, as the number of records in the rectangle goes to infinity the random curves converge conditionally in probability to a non-random limit parametrized curve, which is characterized.

TL;DR: In this paper, the authors consider the behavior of semi-oriented bootstrap percolation restricted to a finite square or torus and show that the side length required for a two-dimensional torus to have non-negligible chance of filling itself up is between for universal constants c and C.

TL;DR: In this paper, the existence, uniqueness and continuity properties of solutions of stochastic Volterra equations with singular integral kernels (driven by Brownian motion) are proven, and the existence and uniqueness properties of such solutions are shown.

TL;DR: In this paper, it was shown that under the bridge law for X starting from 0 and ending at 0 at time t, the amount of time X spends positive has a uniform distribution on [0, t] when 0 is a regular point, leading to an explicit expression for the Laplace transform of the joint distribution of the pair (R, AR).

TL;DR: In this paper, a class of iterated processes is studied by proving a joint functional limit theorem for a pair of independent Brownian motions, and the Strassen method is applied to prove global and local (t → ∞) LIL type results for various iterated process.

TL;DR: In this paper, the authors investigated the tail behavior of the distributions of subadditive functionals of the sample paths of infinitely divisible stochastic processes when the Levy measure of the process has suitably defined exponentially decreasing tails.