Related papers: A Representation Theorem for Smooth Brownian Marti…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general,…
We investigate the global well-posedness and asymptotic behavior of $L^2$-solutions to stochastic nonlinear Schr\"odinger equations with multiplicative noise driven by continuous square integrable martingales with density. Our approach…
Monroe (1978) demonstrates that any local semimartingale can be represented as a time-changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time-change are independent? We prove…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walks, time changed by a discrete quadratic variation process. One basis of this is a similar…
The paper studies a non-linear transformation between Brownian martingales, which is given by the inverse of the pricing operator in the mathematical finance terminology. Subsequently, the solvability of systems of equations corresponding…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
We investigate how the theory of self-adjoint differential equations alone can be used to provide a satisfactory solution of the inverse vatiational problem. For the discrete system, the self-adjoint form of the Newtonian equation allows…
We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by obtained by computing a directional derivative of the weak…
We investigate solutions of backward stochastic differential equations (BSDE) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute the two components of a Levy process. In this new type of…
We describe the classes of functions $f=(f(x), x\in R)$, for which processes $f(W_t)-Ef(W_t)$ and $f(W_t)/Ef(W_t)$ are martingales. We apply these results to give a martingale characterization of general solutions of the quadratic and the…
Simple Exponential Smoothing is a classical technique used for smoothing time series data by assigning exponentially decreasing weights to past observations through a recursive equation; it is sometimes presented as a rule of thumb…
Hamiltonian matrices appear in a variety or problems in physics and engineering, mostly related to the time evolution of linear dynamical systems as for instance in ion beam optics. The time evolution is given by symplectic transfer…
In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the corresponding…
The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this paper. Multiscale techniques are used to derive general formulae for the steady…
Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of…
We construct a fake exponential Brownian motion, a continuous martingale different from classical exponential Brownian motion but with the same marginal distributions, thus extending results of Albin and Oleszkiewicz for fake Brownian…
The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does in general not satisfy an It\^{o} formula like the solution…