Related papers: On quantum stochastic differential equations
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the…
This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…
In this paper we shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst…
The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
We study how to implement quantum stochastic differential equations (QSDEs) on a quantum computer. This is illustrated by an implementation of the QSDE that couples a laser driven two-level atom to the electromagnetic field in the vacuum…
This work presents a complete geometrical characterisation of divisible and indivisible time-evolution at the level of probabilities for systems with two configurations, open or closed. Our new geometrical construction in the space of…
We construct a class of quantum stochastic models of reservoir driven many-particle systems that are the natural counterparts of certain extensively studied classical ones, which have been shown to exhibit good hydrodynamical behaviour. Our…
The aim of this work is to prove existence and uniqueness of $L^{2}-$solutions of stochastic fractional partial differential equations in one spatial dimension. We prove also the equivalence between several notions of $L^{2}-$solutions. The…
In this paper, we prove the existence and uniqueness of the solution for neutral stochastic differential delay equations with locally monotone coefficients by using numerical approximation. An example is provided to illustrate our theory.
The goal of this paper is to clarify when the solutions to stochastic partial differential equations stay close to a given subset of the state space for starting points which are close as well. This includes results for deterministic…
A useful approach is investigated in order to analyze a class of a stochastic differential equations that can be encountered in quantum optics problems, especially, in the case of two photon losses on the driven cavity mode. The passage to…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.
We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to…
The goal of this paper is to provide conditions under which a quantum stochastic differential equation (QSDE) preserves the commutation and anticommutation relations of the SU(n) algebra, and thus describes the evolution of an open n-level…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…