Related papers: Investigation and Development of the Methodologies…
We introduce a novel method for estimating the self-similarity index of a general $H$-self-similar process with either stationary or non-stationary increments. The estimation algorithm is developed based on a modified Lamperti…
The Lamperti transform offers a powerful bridge between self-similar processes and stationary dynamics, making it especially useful for analyzing anomalous diffusion models that lack stationary increments. In this paper we examine the…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
This paper is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly-symmetric stationary…
We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of…
We develop the canonical Volterra representation for a self-similar Gaussian process by using the Lamperti transformation of the corresponding stationary Gaussian process, where this latter one admits a canonical integral representation…
In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem.…
The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this…
We propose a perception imitation method to simulate results of a certain perception model, and discuss a new heuristic route of autonomous driving simulator without data synthesis. The motivation is that original sensor data is not always…
Particle suspensions are ubiquitous in our daily life, but are not well understood due to their complexity. During the last twenty years, various simulation methods have been developed in order to model these systems. Due to varying…
Consider an n-fold integrated Brownian motion. We show that a simple change in time and scale transforms it into a stationary Gaussian process. The collection of stationary processes so constructed not only constitutes an interesting family…
Simulation is a useful tool in situations where training data for machine learning models is costly to annotate or even hard to acquire. In this work, we propose a reinforcement learning-based method for automatically adjusting the…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
Self-similar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating…
Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian.…
Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random…
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian…
We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…
In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the acceptance-rejection method, and it is particularly useful for kinetic…
We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We…