Related papers: Pathwise Solution of a Class of Stochastic Master …
We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…
Advancements in quantum computing have spurred significant interest in harnessing its potential for speedups over classical systems. However, noise remains a major obstacle to achieving reliable quantum algorithms. In this work, we present…
In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…
The state matrix $\rho$ for an open quantum system with Markovian evolution obeys a master equation. The master equation evolution can be unraveled into stochastic nonlinear trajectories for a pure state $P$, such that on average $P$…
We develop a pathwise theory for scalar conservation laws with quasilinear multiplicative rough path dependence, a special case being stochastic conservation laws with quasilinear stochastic dependence. We introduce the notion of pathwise…
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…
By starting from the stochastic Schr\"odinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white…
In a recent work [DDRZ20], it has been developed a novel framework aimed at studying at a perturbative level a large class of non-linear, scalar, real, stochastic PDEs and inspired by the algebraic approach to quantum field theory. The main…
We consider a nonlinear stochastic partial differential equation (SPDE) in divergence form where the forcing term is a Gaussian noise, that is white in time and colored in space such that the gradient of the solution is H\"older-continuous,…
We show that a basic quantum white noise process formally reproduces quantum stochastic calculus when the appropriate normal / chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization…
We continue the development of the theory of pathwise stochastic entropy solutions for scalar conservation laws in $\R^N$ with quasilinear multiplicative ''rough path'' dependence by considering inhomogeneous fluxes and a single rough path…
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these…
Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…
Inspired by applications, we consider reaction-diffusion equations on $\mathbb{R}$ that are stochastically forced by a small multiplicative noise term that is white in time, coloured in space and invariant under translations. We show how…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stochastic Process. Appl., 2016). To this end, we extend the notion of non-linear Young equations to a…
In the late seventies, Clark [In Communication Systems and Random Process Theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) (1978) 721-734, Sijthoff & Noordhoff] pointed out that it would be natural for $\pi_t$, the solution of…
We introduce a probabilistic representation for solutions of quasilinear wave equation with analytic nonlinearities. We use stochastic cascades to prove existence and uniqueness of the solution.
We study quantum filters that are driven by basic quantum noises and construct classical versions. Our approach is based on exploiting the quantum markovian component of the observation and measurement processes of the filters. This…
Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the…