Related papers: Construction of Immigration Superprocesses with De…
Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…
Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed…
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that…
This paper introduces a new class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward…
One of the most efficient ways of generating goal-directed walking motions is synthesising the final motion based on footprints. Nevertheless, current implementations have not examined the generation of continuous motion based on…
We study the asymptotic behaviour of a critical decomposable 3-type Galton-Watson process with immigration when its offspring mean matrix is triangular with diagonal entries 1. It is proved that, under second or fourth order moment…
Timeseries generated from a dynamical source can often be modeled as sample paths of a stochastic differential equation (SDE). The timeseries thus reflects the motion of a particle which flows along the direction provided by a drift /…
We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in the literature and we apply it to the…
We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
We propose a method to construct first integrals of a dynamical system, starting with a given set of independent infinitesimal symmetries. In the case of two infinitesimal symmetries, a rank two Poisson structure on the ambient space it is…
This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process.…
We extend a model for the morphology and dynamics of a crawling eukaryotic cell to describe cells on micropatterned substrates. This model couples cell morphology, adhesion, and cytoskeletal flow in response to active stresses induced by…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
In distributed evolutionary algorithms, migration interval is used to decide migration moments. Nevertheless, migration moments predetermined by intervals cannot match the dynamic situation of evolution. In this paper, a scheme of setting…
We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and…
With remarkable significance in migration prediction, global disease mitigation, urban planning and many others, an arresting challenge is to predict human mobility fluxes between any two locations. A number of methods have been proposed…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing…
By means of an original approach, called "method of the moving frame", we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path dependent…