Showing papers in "Stochastic Processes and their Applications in 2009"

TL;DR: In this article, a generalized pre-averaging approach for estimating the integrated volatility is presented, which can generate rate optimal estimators with convergence rate n 1/4. But the convergence rate is not guaranteed.

TL;DR: In this paper, the authors proposed a new and potentially useful tool called tail process to describe and model extreme values of a stationary, multivariate time series may exhibit dependence across coordinates and over time.

TL;DR: In this paper, a mean-field backward stochastic differential equation (SDE) is studied in a Markovian framework, associated with a McKean-Vlasov forward equation.

TL;DR: In this article, a condition for f-ergodicity of strong Markov processes at a subgeometric rate is provided, couched in terms of a supermartingale property for a functional of the Markov process.

TL;DR: In this article, the authors studied pathwise properties and homeomorphic properties with respect to the initial values for stochastic differential equations driven by G-Brownian motion, and established a Burkholder-Davis-Gundy inequality for the G-stochastic integrals.

TL;DR: In this paper, a Boussinesq model for the Benard convection under random influences is considered as a system of stochastic partial differential equations and large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion.

TL;DR: In this article, a characterization of time consistency in terms of a "cocycle condition" for the minimal penalty function is proved for general dynamic risk measures continuous from above, and the question of the regularity of paths is addressed.

TL;DR: In this article, a gradient-entropy inequality for elliptic diffusion semigroups on complete Riemannian manifolds is established and a global Harnack inequality with power and a heat kernel estimate is derived.

TL;DR: In this article, the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H > 0.5 was shown.

TL;DR: In this paper, Nualart et al. developed the asymptotic theory for the realised power variation of the processes X = ϕ • G, where G is a Gaussian process with stationary increments.

TL;DR: In this paper, a stochastic process whose probability density function is the solution of the fractional Fokker-planck equation with time-dependent drift is constructed, and a strongly and uniformly convergent approximation scheme which allows us to approximate solutions of the FFP equation using Monte Carlo methods is proposed.

TL;DR: In this paper, the authors considered the problem of approximating the tail probability of randomly weighted sums ∑ i = 1 n Θ i X i and their maxima, where X i, i ≥ 1 } is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class.

TL;DR: In this article, the authors consider the signaling game where each node of the decision tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions.

TL;DR: In this article, a new class of estimators for volatility functionals in the setting of frequently observed Itō diffusions which are disturbed by i.i.d. noise is proposed.

TL;DR: In this article, the problem of parameter estimation for generalized Ornstein-Uhlenbeck processes driven by α -stable noises, observed at discrete time instants, was studied and an asymptotically consistent estimator was obtained.

TL;DR: In this article, mild sufficient conditions for exponential ergodicity of a Markov process defined as the solution to a SDE with jump noise are given, including three principal claims: recurrence condition R, topological irreducibility condition S and non-degeneracy condition N, the latter formulated in terms of a certain random subspace of R m, associated with the initial equation.

TL;DR: In this paper, the existence and uniqueness of the mild solutions for stochastic differential equations for Hilbert valued processes are discussed, with the multiplicative noise term given by an integral with respect to a general compensated Poisson random measure.

TL;DR: In this article, necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Levy-driven continuous-parameter ARMA process with index set R are determined.

TL;DR: Flandoli and Romito as discussed by the authors studied the existence of Markov selections for stochastic evolution equations in the absence of uniqueness, and showed that Markov processes can be constructed from a Markov system of processes.

TL;DR: In this paper, it was shown that the free energy of directed polymers in a random environment can be expressed in terms of a sequence of martingale differences relative to a filtration.

TL;DR: In this article, a canonical decomposition of the martingales in the reference filtration as semi-martingale in the enlargement of the reference filter is presented.

TL;DR: In this article, the Skorokhod problem in a time-varying interval is considered and the authors prove existence and uniqueness of the solution. But they also express the solution in terms of an explicit formula and derive two sets of conditions on the moving boundaries.

TL;DR: The martingale characterization of G-Brownian motion has been studied in this article, where a Markov chain is used to construct a G-brownian motion using the martingales in the G-framework.

TL;DR: In this paper, the uniqueness of the solutions of SPDEs with reflection was proved, which was left open in the paper [C. Donati-Martin, E. Pardoux].

TL;DR: In this paper, the authors study the semimartingale property of continuous time moving averages driven by Levy processes and provide necessary and sufficient conditions on the kernel for the moving average to be a semimARTingale in the natural filtration of the Levy process, and when this is the case they also provide a useful representation.

TL;DR: In this article, the authors prove a strong invariance principle for the two-parameter empirical process of stationary sequences under a new weak dependence assumption and give several applications of their results.

TL;DR: In this article, the authors considered some special classes of Levy processes with no gaussian compo- nent whose Levy measure is of the type (dx) = e x (e x 1)dx, where is the density of the stable Levy measure and is a positive parameter which depends on its characteristics.

TL;DR: In this paper, a nonparametric estimation of the Levy density for pure jump Levy processes is proposed, and a bound for the global L 2 -risk restricted to the compact interval is provided.

TL;DR: In this paper, the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations is studied, and it is shown that the maximum likelihood estimator is asymptotically unbiased for the averaging problem, whereas for the homogenization problem maximum likelihood fails unless we subsample the data at an appropriate rate.

TL;DR: In this paper, the boundary Harnack principle is applied to a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in κ-fat open sets (disconnected analogue of John domains).