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A characterization of harmonic sections and a Liouville theorem

Simão Stelmastchuk (2012)

Archivum Mathematicum

Let P ( M , G ) be a principal fiber bundle and E ( M , N , G , P ) an associated fiber bundle. Our interest is to study the harmonic sections of the projection π E of E into M . Our first purpose is give a characterization of harmonic sections of M into E regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of π E .

A counterexample to the smoothness of the solution to an equation arising in fluid mechanics

Stephen Montgomery-Smith, Milan Pokorný (2002)

Commentationes Mathematicae Universitatis Carolinae

We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the ``back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for...

A Metropolis adjusted Nosé-Hoover thermostat

Benedict Leimkuhler, Sebastian Reich (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nosé-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.

A Note on an Application of the Lasota-York Fixed Point Theorem in the Turbulent Transport Problem

Tomasz Komorowski, Grzegorz Krupa (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We study a model of motion of a passive tracer particle in a turbulent flow that is strongly mixing in time variable. In [8] we have shown that there exists a probability measure equivalent to the underlying physical probability under which the quasi-Lagrangian velocity process, i.e. the velocity of the flow observed from the vintage point of the moving particle, is stationary and ergodic. As a consequence, we proved the existence of the mean of the quasi-Lagrangian velocity, the so-called Stokes...

A study of the dynamic of influence through differential equations∗

Emmanuel Maruani, Michel Grabisch, Agnieszka Rusinowska (2012)

RAIRO - Operations Research

The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...

A study of the dynamic of influence through differential equations∗

Emmanuel Maruani, Michel Grabisch, Agnieszka Rusinowska (2012)

RAIRO - Operations Research

The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...

A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion

Kettani, Perla El, Hilhorst, Danielle, Lee, Kai (2017)

Proceedings of Equadiff 14

In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of n with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.

Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections

Romuald Elie, Idris Kharroubi (2014)

ESAIM: Probability and Statistics

This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps via a penalization procedure. This new type of BSDE offers a nice and practical unifying framework to the notions of constrained BSDEs presented in [S. Peng and M. Xu, Preprint. (2007)] and BSDEs...

Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients

Petr Dostál (2022)

Kybernetika

We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded It o processes with bounded coefficients and when the volatility is bounded away from zero.

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