Related papers: A space of generalized Brownian motion path-valued…
In this paper we give some basic and important properties of several typical Banach spaces of functions of $G$-Brownian motion pathes induced by a sublinear expectation--G-expectation. Many results can be also applied to more general…
Path integral representations for generalized Schr\"odinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with L\'evy subordinators is used,…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
We construct a new topology on the space of stopped paths and introduce a calculus for causal functionals on generic domains of this space. We propose a generic approach to pathwise integration without any assumption on the variation index…
This paper establishes a comprehensive theory of geometric rough paths for mixed fractional Brownian motion (MFBM) and its generalized multi-component extensions. We prove that for a generalized MFBM of the form $M_t^H(a) = \sum_{k=1}^N a_k…
In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of…
We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when the energy only depends on increments,…
Work belongs to the most basic notions in thermodynamics but it is not well understood in quantum systems, especially in open quantum systems. By introducing a novel concept of work functional along individual Feynman path, we invent a new…
The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its use as the main driver for price fluctuations,…
In this article, we show that the standard vector-valued generalization of a generalized grey Brownian motion (ggBm) has independent components if and only if it is a fractional Brownian motion. In order to extend ggBm with independent…
An approach to analysis on path spaces of Riemannian manifolds is described. The spaces are furnished with `Brownian motion' measure which lies on continuous paths, though differentiation is restricted to directions given by tangent paths…
The (Feynman) propagator $G(x_2,x_1)$ encodes the entire dynamics of a massive, free scalar field propagating in an arbitrary curved spacetime. The usual procedures for computing the propagator -- either as a time ordered correlator or from…
We introduce a generalized mixed fractional Brownian motion (gmfBm) as a linear combination of two independent fractional Brownian motions with possibly different Hurst indices and investigate conditions under which the time-changed gmfBm…
A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last ten years or so, including, of course, the main…
In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian motion. This process has been introduced by the second author…
Stochastic integration with respect to Gaussian processes, such as fractional Brownian motion (fBm) or multifractional Brownian motion (mBm), has raised strong interest in recent years, motivated in particular by applications in finance,…
Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, which can change the structure of the underlying…
We revise the Levy's construction of Brownian motion as a simple though still rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based "geometrical…
Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is…
In this paper the Feynman path integral technique is applied to two-dimensional spaces of non-constant curvature: these spaces are called Darboux spaces $\DI$--$\DIV$. We start each consideration in terms of the metric and then analyze the…