Biological processes measured repeatedly among a series of individuals are standardly analyzed by mixed models. These biological processes can be adequately modeled by parametric Stochastic Differential Equations (SDEs). We focus on the parametric maximum likelihood estimation of this mixed-effects model defined by SDE. As the likelihood is not explicit, we propose a stochastic version of the E...

First, we prove a necessary and sufficient condition for global in time existence of all solutions of an ordinary differential equation (ODE). It is a condition of one-sided estimate type that is formulated in terms of so-called proper functions on extended phase space. A generalization of this idea to stochastic differential equations (SDE) and parabolic equations (PE) allows us to prove simil...

Stochastic differential equation (SDE) and Fokker-Planck equation (FPE) are two general approaches to describe the stochastic drift-diffusion processes. Solving SDEs relies on the Monte Carlo samplings of individual system trajectory, whereas FPEs describe the time evolution of overall distributions via path integral alike methods. The large state space and required small step size are the majo...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

Self-stabilizing diffusions are stochastic processes, solutions of nonlinear stochastic differential equation, which are attracted by their own law. This specific self-interaction leads to singular phenomenons like non uniqueness of associated stationary measures when the diffusion leaves in some non convex environment (see [5]). The aim of this paper is to describe these invariant measures and...

Specifying time-dependent correlation matrices is a problem that occurs in several important areas of finance and risk management. The goal this work to tackle by applying techniques geometric integration financial mathematics, i.e., combine two fields numerical mathematics have not been studied yet jointly. Based on isospectral flows we create valid matrices, so called flows, solving stochasti...

Transport equation of the galactic cosmic ray (GCR) is numerically solved for qA > 0 and qA < 0 based on the stochastic differential equation (SDE) method. We have developed a fully time-dependent and threedimensional code adapted for the wavy heliospheric current sheet (HCS). Results anticipated by the drift pattern are obtained for sample trajectories and distributions of arrival points at th...

We study a two-dimensional stochastic differential equation that has unique weak solution but no strong solution. show this SDE shares notable properties with Tsirelson’s example of one-dimensional In contrast to equation, which non-Markovian drift, we consider Markov martingale Markovian diffusion coefficient. there is the and natural filtration generated by Brownian motion. also discuss an ap...

It was shown in [J. Bertoin, Ann. Probab. 35, No. 6, 2021 132037] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog. DOI: https://doi...

[1] We thank Lim [2005] for providing this opportunity to clarify the restrictions and confirm the applicability of the results of LaBolle et al. [2000]. LaBolle et al. [2000] develop generalized stochastic differential equations (SDE) that converge to advection dispersion equations with discontinuous dispersion tensor D. The problem of interest here relates to equation (15a) of LaBolle et al. ...