Related papers: A multifractal random walk
We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…
We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences.…
Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…
The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual Minority Game (MG)…
Open quantum random walks (OQRWs) deal with quantum random motions on the line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital…
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
Among the statistical models employed to approximate nonlinear interactions in biological and psychological processes, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, a…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…
Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation…
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one performing a random sampling. Depending on the values of the two…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
We consider the activated random walk (ARW) model where particles follow the path of a general Markov process on a general graph. We prove ARW dominates a simpler process, multiple source internal aggregation (MSIA), and use this to…
This paper studies long range random walks on ${\mathbb{Z}_q}^d$. $X_{t+1} = X_t + Z_t \mod q$, with $(Z_t)$ independent and identically distributed. Multiple entries of $Z_t$ can be non-zero in a transition. An emphasis is on finding the…
We introduce a multidimensional walk with memory and random tendency. The asymptotic behaviour is characterized, proving a law of large numbers and showing a phase transition from diffusive to superdiffusive regimes. In first case, we…
In this work, we propose Random Walk-steered Majority Undersampling (RWMaU), which undersamples the majority points of a class imbalanced dataset, in order to balance the classes. Rather than marking the majority points which belong to the…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…