Related papers: Stochastic bridges of linear systems
We develop a formally exact technique for obtaining steady-state distributions of non-interacting active Brownian particles in a variety of systems. Our technique draws on results from the theory of two-way diffusion equations to solve the…
Consider non-intersecting Brownian motions on the real line, starting from the origin at t=0, with a number of particles forced to reach p distinct target points at time t=1. This work shows that the transition probability, that is the…
We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…
There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include…
Suppose that particles are randomly distributed in $\bR^d$, and they are subject to identical stochastic motion independently of each other. The Smoluchowski process describes fluctuations of the number of particles in an observation region…
We consider the degenerate Einsteins Brownian motion model when the time interval of the moving particles before the collisions, is reciprocal to the number of particles per unit volume u(x,t), at the point of observation x at time t. The…
We study the long-range asymptotic behavior for an out-of-equilibrium countable one-dimensional system of Brownian particles interacting through their rank-dependent drifts. Focusing on the semi-infinite case, where only the leftmost…
We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding stochastic…
We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge…
In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of…
The model consists of a signal process $X$ which is a general Brownian diffusion process and an observation process $Y$, also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process $Y$ is…
The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the…
We consider the overdamped motion of Brownian particles, interacting via particle exclusion, in an external potential that varies with time and space. We show that periodic potentials that maintain specific position-dependent phase…
We design numerical schemes for a class of slow-fast systems of stochastic differential equations, where the fast component is an Ornstein-Uhlenbeck process and the slow component is driven by a fractional Brownian motion with Hurst index…
We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the…
The area enclosed by the two-dimensional Brownian motion in the plane was studied by L\'evy, who found the characteristic function and probability density of this random variable. For other planar processes, in particular ergodic diffusions…
We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the…