Related papers: Brownian subordinators and fractional Cauchy probl…
Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain $D\subset\mathbb{R}^d$…
We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Allouba and Zheng \cite{allouba1}, Baeumer, Meerschaert and Nane…
We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also…
In the last decade the subordinated processes have become popular and found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson…
We introduce a class of interesting stochastic processes based on Brownian-time processes. These are obtained by taking Markov processes and replacing the time parameter with the modulus of Brownian motion. They generalize the iterated…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to…
In this paper, we consider a type of time-changed Markov process, where the time-change is an inverse killed subordinator. This can be seen as an extension of Chen (Chen, Z., Time fractional equations and probabilistic representation, Chaos…
In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…
In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered…
This paper establishes Fokker-Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed…
We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely…
We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to two simpler problems. These Cauchy sub-problems respectively…
The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure and it is related to two generalizations…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed…