Related papers: Conditioning super-Brownian motion on its boundary…
We propose a novel stochastic method to generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time $t_{f}$ under a given potential $U(x)$. These paths are sampled with a probability…
We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching…
We study the precise large deviation probabilities for the sizes of intermediate level sets in branching Brownian motion (BBM). Our conclusions improve a result of A\"{i}dekon, Hu and Shi in [J. Math. Sci. \textbf{238}(2019)]. Additionally,…
We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the…
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…
We study the long-time asymptotics of the probability P_t that the Riemann-Liouville fractional Brownian motion with Hurst index H does not escape from a fixed interval [-L,L] up to time t. We show that for any H \in ]0,1], for both…
We consider the motion of a particle in a force field subjected to adiabatic, fluctuations of external origin. We do not put the restriction on the type of stochastic process that the noise is Gaussian. Based on a method developed earlier…
We consider a gas of independent Brownian particles on a bounded interval in contact with two particle reservoirs at the endpoints. Due to the Brownian nature of the particles, infinitely many particles enter and leave the system in each…
Consider the first exit time of one-dimensional Brownian motion $\{B_s\}_{s\geq 0}$ from a random passageway. We discuss a Brownian motion with two time-dependent random boundaries in quenched sense. Let $\{W_s\}_{s\geq 0}$ be an other…
We consider a model of branching Brownian motion with self repulsion. Self-repulsion is introduced via change of measure that penalises particles spending time in an $\e$-neighbourhood of each other. We derive a simplified version of the…
We discuss the dynamics of single particle by laying a hypothesis that the Hamilton's principle of stationary action is not exact. We then postulate that the deviation of the action with sufficiently short time interval from the stationary…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
In this paper, we are interested in path-dependent stochastic differential equations (SDEs) which are controlled by Brownian motion and its delays. Within this non-Markovian context, we give a H \"ormander-type criterion for the regularity…
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 analyze here different forms of fractional relaxation equations of order {\nu}\in(0,1) and we derive their solutions both in analytical and in probabilistic forms. In particular we show that these solutions can be expressed as crossing…
This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…
A particle moves randomly over the integer points of the real line. Jumps of the particle outside the membrane (a fixed "locally perturbating set") are i.i.d., have zero mean and finite variance, whereas jumps of the particle from the…
We establish high probability estimates on the eigenvalue locations of Brownian motion on the $N$-dimensional unitary group, as well as estimates on the number of eigenvalues lying in any interval on the unit circle. These estimates are…
We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when…