相关论文: Stochastic differential equations for trace-class …
Let $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a selfadjoint Hilbert-Schmidt operator, and $f\in C^n(\mathbb{R})$. We establish that $\varphi(t)=f(A+tK)-f(A)$ is $n$-times continuously differentiable on $\mathbb{R}$ in…
Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle stiff physical terms implicitly is proposed. Both physical and numerical…
In this paper, by using a Taylor development type formula, we show how it is possible to associate differential operators with stochastic differential equations driven by a fractional Brownian motion. As an application, we deduce that…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…
We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in continuously embedded Hilbert spaces with non-smooth…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
The Stochastic Burgers Equation (SBE) is a singular, non-linear Stochastic Partial Differential Equation (SPDE) that describes, on mesoscopic scales, the fluctuations of stochastic driven diffusive systems with a conserved scalar quantity.…
This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…
This paper presents a detailed Lyapunov-based theory to control and stabilize continuously-measured quantum systems, which are driven by Stochastic Schrodinger Equation (SSE). Initially, equivalent classes of states of a quantum system are…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
We establish higher order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator…
We show that the quantum stochastic unitary dynamics Langevin model for continuous in time measurements provides an exact formulation of the Heisenberg uncertainty error-disturbance principle. Moreover, as it was shown in the 80's, this…
In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the…
Trace formulas appear in many forms in noncommutative geometry (NCG). In the first part of this thesis, we obtain results for asymptotic expansions of trace formulas like heat trace expansions by adapting the theory of Multiple Operator…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…