Related papers: Variational principles for the exit time of non-sy…

Minimization variational principles for linear elastodynamic, acoustic, or electromagnetic time-harmonic waves in dissipative media were obtained by Milton, Seppecher and Bouchitt\'e generalizing the quasistatic variational principles of…

In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…

This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…

In this paper, we establish a small time large deviation principles for the quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone.

We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…

In this paper, we discuss the maximum principle for a time-fractional diffusion equation $$ \partial_t^\alpha u(x,t) = \sum_{i,j=1}^n \partial_i(a_{ij}(x)\partial_j u(x,t)) + c(x)u(x,t) + F(x,t),\ t>0,\ x \in \Omega \subset {\mathbb R}^n$$…

We derive diffusion constants and martingales for senile random walks with the help of a time-change. We provide direct computations of the diffusion constants for the time-changed walks. Alternatively, the values of these constants can be…

This article is accepted for publication in the "Annals I.H.P. Prob. & Stat.". We investigate the ballistic behavior of diffusions in random environment. We introduce conditions in the spirit of (T) and (T') of the discrete setting, cf.…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…

The analytic continuation from the Euclidean domain to real space of the one-particle irreducible quantum effective action is discussed in the context of generalized local equilibrium states. Discontinuous terms associated with dissipative…

We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…

This paper is concerned with a central limit theorem for quadratic variation when observations come as exit times from a regular grid. We discuss the special case of a semimartingale with deterministic characteristics and finite activity…

Using Onsager's variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. The elimination of the extra variable that is coupled to the nonequilibrium driving force leads to the…

Fluctuations arising in nonlinear dissipative systems (diode, transistors, chemical reaction, etc.) subject to an external drive (voltage, chemical potential, etc.) are well known to elude any simple characterization such as the…

A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…

In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential…

In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a…

Barotropic fluid flows with the same circulation structure as steady flows generically have comoving physical surfaces on which the vortex lines lie. These become Bernoullian surfaces when the flow is steady. When these surfaces are nested…

We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…