Related papers: A class of spatio-temporal and causal stochastic p…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
We present a dynamical log-stable process for the spatio-temporal evolution of the energy-dissipation field in fully developed turbulence. The process is constructed from multifractal scaling relations required for two-point correlators of…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Multiplicative cascades have been used in turbulence to generate fields with multifractal statistics and long-range correlations. Examples of continuous and causal stochastic processes which generate such a random field have been carefully…
The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time…
We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we…
The n-point statistics of singularity strength variables for multiplicative branching processes is calculated from an analytic expression of the corresponding multivariate generating function. The key ingredient is a branching generating…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently…
We consider the spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We study the pathwise properties of the stochastic process $(V_t)_{t\geq 0}$, which describes the time evolution of the velocity of a…
In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model…
Longitudinal studies with binary or ordinal responses are widely encountered in various disciplines, where the primary focus is on the temporal evolution of the probability of each response category. Traditional approaches build from the…
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, based on a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated…
The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
The dynamic and kinetic behavior of processes occurring in fractals with spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the existence of a fundamental scaling ratio (b_1). We address time-dependent physical…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…