Related papers: A Complex Version of G-Expectation and its Applica…
We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…
This is an extended version of the lecture notes to a mini-course devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop.
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H>1/2 as a typical example. We establish infinite and finite past…
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
This work presents higher order Lagrangian dynamics possessing locally conformal character. More concretely, locally conformal higher order Euler-Lagrange equations are written with particular focus on the second- and the third-order cases.
A regression method for proportional, or fractional, data with mixed effects is outlined, designed for analysis of datasets in which the outcomes have substantial weight at the bounds. In such cases a normal approximation is particularly…
Consider an n-fold integrated Brownian motion. We show that a simple change in time and scale transforms it into a stationary Gaussian process. The collection of stationary processes so constructed not only constitutes an interesting family…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach space $X$. The present paper is an application of one the…
We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We…
This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…
We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semi-martingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the…
We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provide necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem…
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. We review some main convergence results, conjectures and problems in the construction and study of…
The acceleration transformations form a 4-parameter Abelian subgroup of the conformal group of Minkowski spacetime. The passive interpretation of acceleration transformations leads to a congruence of uniformly accelerated observers in…
Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness…
In this paper, we study the discrete-time approximation schemes for a class of backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) which corresponds to the hedging pricing of European contingent claims. By…
We investigate the rate functions that emerge in our previous works towards large deviation principle for the matrix liberation process driven by the unitary Brownian motion as well as the unitary Brownian motion itself. Our approach is…
This article presents various weak laws of large numbers for the so-called realised covariation of a bivariate stationary stochastic process which is not a semimartingale. More precisely, we consider two cases: Bivariate moving average…