Abstract. In this paper we discuss the existence of PC-mild solutions for Cauchy problems and nonlocal problems for impulsive fractional evolution equations involving Caputo fractional derivative. By utilizing the theory of operators semigroup, probability density functions via impulsive conditions, a new concept on a PC-mild solution for our problem is introduced. Our main techniques based on ...

This paper describes some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals are defined with explicit expressions for their first two moments. Multiple and iterated integrals of a fractional Browinian motion are defined and various properties of these integrals are given. A square integrab...

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of comp...

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the ge...

Besides fractional Brownian motion most non-Gaussian fractional fields are obtained by integration of deterministic kernels with respect to a random infinitely divisible measure. In this paper, generalized shot noise series are used to obtain approximations of most of these fractional fields, including linear and harmonizable fractional stable fields. Almost sure and Lr-norm rates of convergenc...

For any discrete-time P–local martingale S there exists a probability measure Q ∼ P such that S is a Q–martingale. A new proof for this result is provided. This proof also yields that, for any ε > 0, the measure Q can be chosen so that dQ/dP ≤ 1 + ε.

In this paper, we study a parametric class of stochastic processes to model both fast and slow anomalous diffusions. This class, called generalized grey Brownian motion (ggBm), is made up of self-similar with stationary increments processes (H-sssi) and depends on two real parameters α ∈ (0, 2) and β ∈ (0, 1]. It includes fractional Brownian motion when α ∈ (0, 2) and β = 1, and time-fractional...