Related papers: An anticipating It\^o formula for L\'evy processes

We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It…

This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel…

We define a L\'evy process on a smooth manifold $M$ with a connection as a projection of a solution of a Marcus stochastic differential equation on a holonomy bundle of $M$, driven by a holonomy-invariant L\'evy process on a Euclidean…

This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that…

We introduce an elementary method for proving the absolute continuity of the time marginals of one-dimensional processes. It is based on a comparison between the Fourier transform of such time marginals with those of the one-step Euler…

This paper considers the class of L\'evy processes that can be written as a Brownian motion time changed by an independent L\'evy subordinator. Examples in this class include the variance gamma model, the normal inverse Gaussian model, and…

The goal of this paper is to investigate how the marginal and dependence structures of a variety of multivariate L\'evy models affect calibration and pricing. To this aim, we study the approaches of Luciano and Semeraro (2010) and Ballotta…

These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.

Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from…

We treat a stochastic integration theory for a class of Hilbert-valued, volatility-modulated, conditionally Gaussian Volterra processes. We apply techniques from Malliavin calculus to define this stochastic integration as a sum of a…

Chen, Fitzsimmons, Kuwae and Zhang (Ann. Probab. 36 (2008) 931-970) have established an Ito formula consisting in the development of F(u(X)) for a symmetric Markov process X, a function u in the Dirichlet space of X and any…

The article is devoted to the expansion of iterated Ito stochastic integrals of second multiplicity based on expansion of the Brownian motion (standard Wiener process) using complete orthonormal systems of functions in the space $L_2([t,…

This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out…

In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at…

L\'evy copulas are an important tool which can be used to build dependent L\'evy processes. In a classical setting, they have been used to model financial applications. In a Bayesian framework they have been employed to introduce dependent…

In this paper, we propose a fast and accurate numerical method based on Fourier transform to solve Kolmogorov forward equations of symmetric scalar L\'evy processes. The method is based on the accurate numerical formulas for Fourier…

It is known that the exponential functional of a Poisson process admits a probability density function in the form of an infinite series. In this paper, we obtain an explicit expression for the density function of the exponential functional…

We present a class of L\'evy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated L\'evy…

In this paper, we establish a probabilistic representation for two integration by parts formulas, one being of Bismut-Elworthy-Li's type, for the marginal law of a one-dimensional diffusion process killed at a given level. These formulas…