Related papers: Feynman-Kac Kernels in Markovian Representations o…
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman-Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different…
The purpose of this comment is to correct mistaken assumptions and claims made in the paper Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations by T. D. Frank. Our comment centers on the claims…
A discrete rate theory for general multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three…
In the framework of stochastic functional differential equations (SFDE's) and the corresponding calculus developed in the recent years by F. Yan and S. Mohammed, we provide a series of representation formulae for a variety of highly…
We show that a formal solution of a rather general non-Markovian Fokker-Planck equation can be represented in a form of an integral decomposition and thus can be expressed through the solution of the Markovian equation with the same…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
In this paper we study time-inhomogeneous versions of one-dimensional Stochastic Differential Equations (SDE) involving the Local Time of the unknown process on curves. After proving existence and uniqueness for these SDE under mild…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
We consider different Markovian embedding schemes of non-Markovian stochastic processes that are described by generalized Langevin equations (GLE) and obey thermal detailed balance under equilibrium conditions. At thermal equilibrium…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
Consider the following mechanism for the random evolution of a distribution of mass on the integer lattice ${\mathbf{Z}}$. At unit rate, independently for each site, the mass at the site is split into two parts by choosing a random…
Schr\"{o}dinger bridge is a diffusion process that steers a given distribution to another in a prescribed time while minimizing the effort to do so. It can be seen as the stochastic dynamical version of the optimal mass transport, and has…
E. Schroedinger proposed the equation to find the statistical property of a quantum particle on a finite time interval. It is called "Schroedinger's functional equation". Given probability distributions of a particle at initial and terminal…
We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, describing a generic model of variable media, in the case of multi-parameter squeezed input photon configuration. The corresponding probability…
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…
The main results of this paper comprise proofs of the following two related facts: (i) the Feynman--Kac formula is a functor $F_*$, namely, between a stochastic differential equation and a dynamical system on a statistical manifold, and…
In this work, we consider a one-dimensional It{\^o} diffusion process X t with possibly nonlinear drift and diffusion coefficients. We show that, when the diffusion coefficient is known, the drift coefficient is uniquely determined by an…
In the first part of the paper we prove various results on regularity of Feynman-Kac functionals of Hunt processes associated with time dependent semi-Dirichlet forms. In the second part we study the Cauchy problem for semilinear parabolic…
We prove that the solution of the Hudson-Parthasarathy quantum stochastic differential equation in the Fock space coincides with the solution of a symmetric boundary value problem for the Schr\"odinger equation in the interaction…
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. In the particular cases the solutions of such an equations are the well-known…