Related papers: On the Martingale Representation with Respect to t…

The Dirac-Born-Infled action that describes the dynamics of D branes also allows one to compute the supersymmetries they preserve using the Kappa-symmetry projector. The ''Lagrangian'' expression of this projector depends on the velocity…

We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex…

This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper in J.…

In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration (this condition is a generalization of the classical relation 1 + i^2 = 0 in…

The purpose of this paper is to establish a variational representation \log \E [e^{f(B)}] = \sup_h \E [f(B + \int_0^{\cdot} d<B>_s h_s) - 1/2 \int_0^1 h_s \cdot (d<B>_s h_s)] for functionals of the d-dimensional G-Brownian motion B. Here \E…

This preprint is dedicated to a self contained simple proof of the classical criteria for representability of algebraic functions of several complex variables by radicals. It also contains a criteria for representability of algebroidal…

An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…

In this article, we develop a semigroup-theoretic framework for the analytic characterisation of martingales with path-dependent terminal conditions. Our main result establishes that a measurable adapted process of the form \[ V(t) -…

In this note we introduce some nonlinear extremal nonlocal operators that approximate the, so called, truncated Laplacians. For these operators we construct representation formulas that lead to the construction of what, with an abuse of…

Comparison results for Markov processes w.r.t. function class induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach…

We define a time dependent empirical process based on $n$ independent fractional Brownian motions and describe strong approximations to it by Gaussian processes. They lead to strong approximations and functional laws of the iterated…

Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion…

We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem,…

In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.

This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…

We prove the transfer principle for fractional Ornstein-Uhlenbeck processes, i.e., we construct a Brownian motion that has the same filtration as the fractional Ornstein-Uhlenbeck process and then represent the fractional Ornstein-Uhlenbeck…

This paper is a direct continuation of the paper arXiv:2401.00053. By this reason neither introductory part of the paper nor the list of references are not duplicated. However for the reader convenience, the formulas from the first paper…

It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…

Within the framework of the theory of quaternion column-row determinants and using determinantal representations of the Moore-Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of…