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We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be…

Computational Finance · Quantitative Finance 2009-10-28 Roman N. Makarov , Devin Glew

We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…

Probability · Mathematics 2015-09-30 Laurent Decreusefond , Ian Flint , Nicolas Privault , Giovanni Luca Torrisi

.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…

Statistical Mechanics · Physics 2020-08-26 V. Sposini , D. S. Grebenkov , R. Metzler , G. Oshanin , F. Seno

This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…

We provide a stochastic fractional diffusion equation description of energy transport through a finite one-dimensional chain of harmonic oscillators with stochastic momentum exchange and connected to Langevian type heat baths at the…

Statistical Mechanics · Physics 2019-05-22 Aritra Kundu , Cédric Bernardin , Keji Saito , Anupam Kundu , Abhishek Dhar

In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary…

Classical Analysis and ODEs · Mathematics 2015-06-25 Ahmet Gökdoğan , Emrah Ünal , Ercan Çelik

Heterogeneous diffusion processes are prevalent in various fields, including the motion of proteins in living cells, the migratory movement of birds and mammals, and finance. These processes are often characterized by time-varying dynamics,…

Statistical Mechanics · Physics 2025-03-11 Michał Balcerek , Adrian Pacheco-Pozo , Agnieszka Wyłomańska , Diego Krapf

A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…

Probability · Mathematics 2014-03-13 Bruno Saussereau

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…

Analysis of PDEs · Mathematics 2016-11-29 Jebessa B. Mijena , Erkan Nane

This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…

Numerical Analysis · Mathematics 2023-06-05 Ashish Rayal , Bhagawati Prasad Joshi , Mukesh Pandey , Delfim F. M. Torres

The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable replaced by a stable subordinator and its…

Probability · Mathematics 2016-08-09 Luisa Beghin , Costantino Ricciuti

We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…

Statistics Theory · Mathematics 2020-04-10 Jean-Charles Croix , Masoumeh Dashti , Istvàn Zoltàn Kiss

The effect of particle-nonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized ABC model. It is shown that in the limit of slow nonconserving processes, the large deviation…

Statistical Mechanics · Physics 2012-02-17 Or Cohen , David Mukamel

We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream teacher and then pass samples from the model to their downstream student. It extends the population dynamics…

Populations and Evolution · Quantitative Biology 2012-02-28 James P. Crutchfield , Sean Whalen

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Machine Learning · Statistics 2017-08-09 Constantino A. García , Abraham Otero , Paulo Félix , Jesús Presedo , David G. Márquez

In this paper, we investigate the stationarity of stochastic processes in the fractional Fourier domains. We study the stationarity of a stochastic process after performing fractional Fourier transform (FRFT), and discrete fractional…

Complex Variables · Mathematics 2012-11-13 Ahmed El Shafie , Tamer Khattab

In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…

Probability · Mathematics 2016-09-08 Young Myoung Ko , Natarajan Gautam

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…

Statistical Mechanics · Physics 2015-05-14 Valery Ilyin , Itamar Procaccia , Anatoly Zagorodny

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

Numerical Analysis · Mathematics 2022-04-12 Kai Diethelm

The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the…

Statistical Mechanics · Physics 2009-06-02 E. Heinsalu , M. Patriarca , I. Goychuk , P. Hanggi