Related papers: The method of decoupling fields generalized to hig…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…
We shall study backward stochastic differential equations and we will present a new approach for the existence of the solution. This type of equation appears very often in the valuation of financial derivatives in complete markets.…
The study of decoherence plays a key role in our understanding of the transition from the quantum to the classical world. Typically, one considers a system coupled to an external bath which forms a model for an open quantum system. While…
We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way…
We solve the problem of formulating Brownian motion in a relativistically covariant framework in 1+1 and 3+1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of invariant…
We study the stochastic dynamics of a Brownian particle after it is suddenly released from a harmonic trap moving with constant velocity through a fluctuating correlated medium, described by a scalar Gaussian field with relaxational…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation…
It is shown how to construct a successful co-adapted coupling of two copies of an $n$-dimensional Brownian motion $(B_1,...,B_n)$ while simultaneously coupling all corresponding copies of L\'{e}vy stochastic areas $\int B_i dB_j-\int B_j…
We investigate the entanglement of a quantum field in the expanding universe. By introducing a bipartite system using a coarse-grained scalar field, we apply the separability criterion based on the partial transpose operation and…
Usually when applying the mimetic model to the early universe, higher derivative terms are needed to promote the mimetic field to be dynamical. However such models suffer from the ghost and/or the gradient instabilities and simple…
This research concerns coefficient conditions for linear differential equations in the unit disc of the complex plane. In the higher order case the separation of zeros (of maximal multiplicity) of solutions is considered, while in the…
We consider the model space of constant curvature in dimension n and characterize all co-adapted couplings of Brownian motions on this space for which the distance between the processes is deterministic. In addition, the construction of the…
Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is…
A general method is discussed to obtain Markovian master equations which describe the interaction with the environment in a microscopic and non-perturbative fashion. It is based on combining time-dependent scattering theory with the concept…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of d'Alembert form. Treating…
We solve the model of N quantum Brownian oscillators linearly coupled to an environment of quantum oscillators at finite temperature, with no extra assumptions about the structure of the system-environment coupling. Using a compact…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap…