Control of Mammalian Circadian Rhythm by CKIε-Regulated Proteasome-Mediated PER2 Degradation Erik J. Eide, Margaret F. Woolf, Heeseog Kang, Peter Woolf, William Hurst, Fernando Camacho, Erica L. Vielhaber, Andrew Giovanni, and David M. Virshup* Department of Oncological Sciences and the Center for Children, Huntsman Cancer Institute, and Division of Hematology/Oncology, Department of Pediatrics...

In this paper we establish the existence of path-wise solutions and the uniqueness in law for multidimensional stochastic differential equations driven by a multi-dimensional fractional Brownian motion with Hurst parameter H > 12 .

This paper presents a study of the Hurst index estimation in the case of fractional Ornstein–Uhlenbeck and geometric Brownian motion models. The performance of the estimators is studied both with respect to the value of the Hurst index and the length of sample paths.

This paper presents empirical evidence of long range dependence in returns and volatility for banking indices for 41 different countries. We employ the Rescaled Hurst analysis and develop a formal statistical procedure to test for long range dependence. This procedure allows to rank these countries by relative inefficiency, which can provide guidance for investors and portfolio managers. Keywor...

Let {{XH(t), t ∈ RN}, H ∈ (0, 1)N} be a family of (N, d)-anisotropic Gaussian random fields with generalized Hurst indices H = (H1, . . . ,HN ) ∈ (0, 1) . Under certain general conditions, we prove that the local time of {XH0(t), t ∈ RN} is jointly continuous whenever ∑N `=1 1/H 0 ` > d. Moreover we show that, when H approaches H , the law of the local times of X(t) converges weakly [in the spa...

We introduce a natural family of random walks Sn on Z that scale to fractional Brownian motion. The increments Xn := Sn − Sn−1 ∈ {±1} have the property that given {Xk : k < n}, the conditional law of Xn is that of Xn−kn , where kn is sampled independently from a fixed law μ on the positive integers. When μ has a roughly power law decay (precisely, when μ lies in the domain of attraction of an α...

We study the two-dimensional fractional Brownian motion with Hurst parameter H > 1 2. In particular, we show, using stochastic calculus , that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.

In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter H > 1/2. Our results rely on recent tools of Young integration for convolutional integrals combined with stochastic analysis methods for the study of laws of random variables defined on a Wiener sp...

The conventional formal tool to detect effects of the financial persistence is in terms of the Hurst exponent. A typical corresponding result is that its value comes out close to 0.5, as characteristic for geometric Brownian motion, with at most small departures from this value in either direction depending on the market and on the time scales involved. We study the high frequency price changes...

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2 < H < 1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized selfintersection lo...