Related papers: Stochastic calculus over symmetric Markov processe…

It is shown that non-Markovian master equations for an open system which are local in time can be unravelled through a piecewise deterministic quantum jump process in its Hilbert space. We derive a stochastic Schr\"odinger equation that…

We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…

This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…

Given a reference filtration $\mathbb{F}$, we develop in this work a generic method for computing the semimartingale decomposition of $\mathbb{F}$-martingales in some specific enlargements of $\mathbb{F}$. This method is then applied to the…

By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. In this new notion of adaptedness,``classical'' time…

We consider a Markov additive process with a finite phase space and study its path decompositions at the times of extrema, first passage and last exit. For these three families of times we establish splitting conditional on the phase, and…

Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the…

This paper discusses tractable development and statistical estimation of a continuous time stochastic process with a finite state space having non-Markov property. The process is formed by a finite mixture of right-continuous Markov jump…

We prove generalizations of the first and second Ray-Knight theorems, for a large class of non-symmetric strong Markov processes. These results link the local times of the Markov process with the squares of associated Gaussian processes.…

In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the…

An analogue of the Fourier transform will be introduced for all square integrable continuous martingale processes whose quadratic variation is deterministic. Using this transform we will formulate and prove a stochastic Heisenberg…

Advances in sampling schemes for Markov jump processes have recently enabled multiple inferential tasks. However, in statistical and machine learning applications, we often require that these continuous-time models find support on…

We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by "controlled" Markov noise. In particular, the faster and slower recursions have non-additive controlled Markov noise…

In this paper we propose an efficient variance reduction approach for additive functionals of Markov chains relying on a novel discrete time martingale representation. Our approach is fully non-asymptotic and does not require the knowledge…

We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…

We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an approximation scheme in which the continuous path dependence…

A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang's maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the…

In this paper, we study darning of general symmetric Markov processes by shorting some parts of the state space into singletons. A natural way to construct such processes is via Dirichlet forms restricted to the function space whose members…