Related papers: Time-reversibility and nonvanishing Levy area
Time-consistency is an essential requirement in risk sensitive optimal control problems to make rational decisions. An optimization problem is time consistent if its solution policy does not depend on the time sequence of solving the…
In this paper, we solve exit problems for a L\'evy process that resets proportionally to its current position at independent Poisson epochs times. This resetting causes an additional (proportional to its current level) downward (upward)…
We address the inviscid limit for the Navier-Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and has finite Sobolev regularity in the complement. We prove that for such data…
In this paper we consider a class of continuity equations that are conditioned to stay in general space-time domains, which is formulated as a continuum limit of interacting particle systems. Firstly, we study the well-posedness of the…
Mittag-Leffler condition ensures the exactness of the inverse limit of short exact sequences indexed on a partially ordered set $(I,\leq)$ admitting a $countable$ cofinal subset. We extend Mittag-Leffler condition by relatively relaxing the…
In this article we study a class of stochastic functional differential equations driven by L\'{e}vy processes (in particular, $\alpha$-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals.…
This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that stable identifiability is possible if the upper uniform…
In this paper we establish a sharp non-uniqueness result for stochastic $d$-dimensional ($d\geq2$) incompressible Navier-Stokes equations. First, for every divergence free initial condition in $L^2$ we show existence of infinite many global…
The article is devoted to the expansion of iterated Ito stochastic integrals of second multiplicity based on expansion of the Brownian motion (standard Wiener process) using complete orthonormal systems of functions in the space $L_2([t,…
The solutions of stochastic differential equations without an external drift are stochastically invariant under time reversal. This singles out the "anti-Ito" integral.
We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be H\"older regular in space and evolve continuously in time. The inverse operator is of Bogovskij type,…
Dynamical localization is a localization phenomenon taking place, for example, in the quantum periodically-driven kicked rotor. It is due to subtle quantum destructive interferences and is thus of intrinsic quantum origin. It has been shown…
We prove boundedness and inverse logarithmic decay in time of solutions to the Teukolsky equations on Schwarzschild-Anti-de Sitter backgrounds with standard boundary conditions originating from fixing the conformal class of the non-linear…
We discuss the Gamma Levy process, including path properties, the inverse process, integrability, and its spin-offs obtained by compounding, exponentiation, and other operations; further extendable to arbitrary sigma-finite continuous Borel…
We investigate a class of stochastic integro differential equations driven by Levy noise.
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
We study the almost sure asymptotic behavior of the supremum of the local time for a transient diffusion in a spectrally negative L\'evy environment. More precisely, we provide the proper renormalizations for the extremely large and the…
This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…
The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{-1/4}$ as time $t$ goes to infinity. This improves the works [Selberg, da Silva, Lower…
We show that the geometric structure of an arbitrary relativistic spacetime can be determined by the transformation groups associated with a collection of privileged coordinate systems.