Conditional characteristic functions of processes related to fractional Brownian motion

Conditional Characteristic Functions of Molchan-Golosov Fractional Lévy Processes with Application to Credit Risk

Molchan-Golosov fractional Lévy processes (MG-fLps) are introduced by a multivariate componentwise Molchan-Golosov transformation based on an n-dimensional driving Lévy process. Using results of fractional calculus and infinitely divisible distributions we are able to calculate the conditional characteristic function of integrals driven by MG-fLps. This leads to important prediction results inc...

Prediction of fractional convoluted Lévy processes with application to credit risk

Fractional convoluted Lévy processes (fcLps) are introduced by a multivariate componentwise Molchan-Gosolov transformation based on an n-dimensional driving Lévy process. Using results of fractional calculus and infinitely divisible distributions we are able to calculate the conditional characteristic function of integrals driven by fcLps. This leads to important prediction results including th...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Self-Similarity: Part II-Optimal Estimation of Fractal Processes

In a companion paper we characterized the class of scale-invariant convolution operators: the generalized fractional derivatives of order γ. We used these operators to specify regularization functionals for a series of Tikhonov-like least squares data fitting problems and proved that the general solution is a fractional spline of twice the order. We investigated the deterministic properties of ...

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory