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In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite (αN) and sampled under two different random times. Based on the limit behavior of the characteristic function and convergence result we prove the asymptotic normality for the least square estimator. We present simulations results to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

We study the solution to the stochastic wave equation with Dirichlet boundary conditions driven by a Gaussian noise which behaves as a fractional Brownian motion in time and as a Wiener process in space. We obtain the existence of the solution as well as various other properties (pathwise regularity, scaling properties, or the behavior with respect to the Hurst parameter). [ABSTRACT FROM AUTHOR]

We define power variation estimators for the drift parameter of the stochastic heat equation with the fractional Laplacian and an additive Gaussian noise which is white in time and white or correlated in space. We prove that these estimators are consistent and asymptotically normal and we derive their rate of convergence under the Wasserstein metric. [ABSTRACT FROM AUTHOR]

We consider a d -parameter Hermite process with Hurst index H = (H 1 ,.. , H d) ∈ 1 2 , 1 d and we study its limit behavior in distribution when the Hurst parameters H i , i = 1 ,.. , d (or a part of them) converge to 1 2 and/or 1. The limit obtained is Gaussian (when at least one parameter tends to 1 2) and non-Gaussian (when at least one-parameter tends to 1 and none converges to 1 2). [ABSTRACT FROM AUTHOR]

Let be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process with respect to the time and to the space variable, respectively. In particular, we derive exact uniform moduli of continuity and Chung-type laws of iterated logarithm. [ABSTRACT FROM AUTHOR]

In 1962 Lamperti introduced a transformation that associates to every non-trivial self-similar process a strictly stationary process. This transform has been widely studied for Gaussian processes and in particular for fractional Brownian motion. Our aim is to analyze various properties of the Lamperti transform of the fractional Brownian sheet. We give the stochastic differential equation satisfied by this transform and we represent it as a series of independent Ornstein-Uhlenbeck sheets. [ABSTRACT FROM AUTHOR]

We consider the transport equation driven by the fractional Brownian motion. We study the existence and the uniqueness of the weak solution and, by using the tools of the Malliavin calculus, we prove the existence of the density of the solution and we give Gaussian estimates from above and from below for this density. [ABSTRACT FROM AUTHOR]

We study the law of the solution to the stochastic heat equation with additive Gaussian noise which behaves as the fractional Brownian motion in time and is white in space. We prove a decomposition of the solution in terms of the bifractional Brownian motion. Our result is an extension of a result by Swanson. [ABSTRACT FROM AUTHOR]

We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion. Using the techniques of the Malliavin calculus, we study the existence of this object and its properties. We then propose a continuous time model for financial modeling that captures the main properties observed in the empirical data, including the leverage effect. We illustrate our result by numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the least squares estimator for the drift parameter of an infinite-dimensional fractional Ornstein–Uhlenbeck process with Hurst parameter . This estimator can be expressed in terms of a divergence integral with respect to the fractional Brownian motion. Using some recently developed criteria based on Malliavin calculus and Wiener–Itô chaos expansion, we prove the strong consistency and the asymptotic normality of the estimator. [Copyright &y& Elsevier]

In this paper, we establish the existence of a square integrable occupation density for two classes of stochastic processes. First, we consider a Gaussian process with an absolutely continuous random drift, and second, we handle the case of a (Skorohod) integral with respect to the fractional Brownian motion with Hurst parameter [image omitted] . The proof of these results uses a general criterion for the existence of a square integrable local time, which is based on the techniques of Malliavin calculus. [ABSTRACT FROM AUTHOR]

Abstract: By using Malliavin calculus and multiple Wiener–Itô integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces with its regularity in the Watanabe spaces. [Copyright &y& Elsevier]

Abstract: This paper is devoted to analyzing several properties of the bifractional Brownian motion introduced by Houdré and Villa. This process is a self-similar Gaussian process depending on two parameters and and it constitutes a natural generalization of fractional Brownian motion (which is obtained for ). Here, we adopt the strategy of stochastic calculus via regularization. Of particular interest to us is the case . In this case, the process is a finite quadratic variation process with bracket equal to a constant times and it has the same order of self-similarity as standard Brownian motion. It is a short-memory process even though it is neither a semimartingale nor a Dirichlet process. [Copyright &y& Elsevier]

In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q ≥ 2 of the fractional Brownian motion with Hurst parameter H ϵ (0, 1), where q is an integer. The central limit holds for 1/2q < H ≤ 1 - 1/2q, the limit being a conditionally Gaussian distribution. If H < 1/2q we show the convergence in L2 to a limit which only depends on the fractional Brownian motion, and if H > 1 - 1/2q we show the convergence in L² to a stochastic integral with respect to the Hermite process of order q. [ABSTRACT FROM AUTHOR]