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We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions th...
We study the existence and azimuthal modulational stability of vortices in the two-dimensional (2D) cubic-quintic nonlinear Schr¨odinger (CQNLS) equation. We use a variational approximation (VA) based...
We study the existence and stability of multisite discrete breathers in two prototypical non-square Klein–Gordon lattices, namely a honeycomb and a hexagonal one. In the honeycomb case we consider six...
We consider finite-dimensional multivalued stochastic differential equations where the drift has a multivalued and monotone term. Existence and approximation results are obtained by an existence th...
We consider the one-dimensional stochastic equation for a continuous local martingale M with square variation {M) and measurable drift and diffusion coefficients b and F. The main purpose of this p...
Let (M,),,,be an ergodic Markov chain on a general state space X with stationary distribution n and g: X + [0, m) a meadef surable function. D&e So (g) = 0 and S,(g) g (MI+). . .+g(M.) for n 3 1. ...
In the present article we consider a model of motion of a passive tracer particle under a random, non-steady (time dependent), incompressible velocity flow in a medium with positive molecular diffus...
In the present paper we consider a continuous time random walk on an anisotropic random lattice. We show the existence of a steady state 0, for the environment process (( (t)),ao corresponding to t...
Existence and Regularity of Solutions to a Stochastic Burgers-Type Equation。
We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affe...
We deal with multidimensional backward stochastic differential equations (BSDE) with locally Lipschitz coefficient in both variables $ y,z $ and an only square integrable terminal data. Let $ L_N $ be...
Let X = (Xt)t ≥ 0 be a self-similar Markov process with values in the non-negative half-line, such that the state 0 is a trap. We present a necessary and sufficient condition for the existence of a se...
We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in ...

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