相关论文: Multifractal analysis for the occupation measure o…
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses…
Let $\Gamma$ act on a countable set V with only finitely many orbits. Given a $\Gamma$-invariant random environment for a Markov chain on V and a random scenery, we exhibit, under certain conditions, an equivalent stationary measure for the…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
A stochastic process $X$ becomes occupied when it is enlarged with its occupation flow $\mathcal{O}$ that tracks the time spent by the path at each level. When $X$ is Markov, the occupied process $(\mathcal{O},X)$ enjoys a Markov structure…
Multifractal analysis is a forecasting technique used to study the scaling regularity properties of financial returns, to analyze the long-term memory and predictability of financial markets. In this paper, we propose a novel structural…
The multifractal spectrum of a Borel measure $\mu$ in $\mathbb{R}^n$ is defined as \[ f_\mu(\alpha) = \dim_H {x:\lim_{r\to 0} \frac{\log \mu(B(x,r))}{\log r}=\alpha}. \] For self-similar measures under the open set condition the behavior of…
The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of disordered systems, notably from the…
Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We propose a difference-based approach for a one-dimensional…
A real harmonizable multifractional stable process is defined, its H\"older continuity and localizability are proved. The existence of local time is shown and its regularity is established.
This paper considers the problem of sensory data scheduling of multiple processes. There are $n$ independent linear time-invariant processes and a remote estimator monitoring all the processes. Each process is measured by a sensor, which…
Quasiperiodic moir\'e materials provide a new platform for realizing critical electronic states, yet a direct and experimentally practical method to characterize this criticality has been lacking. We show that a multifractal analysis of the…
We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values…
Occupancy processes are a broad class of discrete time Markov chains on $\{0,1\}^{n}$ encompassing models from diverse areas. This model is compared to a collection of $n$ independent Markov chains on $\{0,1\}$, which we call the…
In this work, we investigate the H\"older spectrum of typical measures (in the Baire category sense) in a general compact set and we compute the multifractal spectrum of a typical measures supported by a self-similar set. Such mesures…
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these…
We propose the application of occupation measure theory to the classical problem of transient stability analysis for power systems. This enables the computation of certified inner and outer approximations for the region of attraction of a…
Smoothness and asymptotic behaviors are studied for the densities of the law of the occupation time on the positive line for Bessel bridges and the normalized excursion of strictly stable processes. The key role is played by these…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
We study the transformed path measure arising from the self-interaction of a three-dimensional Brownian motion via an exponential tilt with the Coulomb energy of the occupation measures of the motion by time $t$. The logarithmic asymptotics…