相关论文: The coding complexity of L\'evy processes
In this article, we explore some of the main mathematical problems connected to multidimensional fractional conservation laws driven by L\'evy processes. Making use of an adapted entropy formulation, a result of existence and uniqueness of…
The main goal of the work is to study the stochastic averaging principle for two time-scales stochastic evolution equations driven by L\'evy process. The solution of reduced equation with modified coefficient is derived to approximate the…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
We characterize the small-time asymptotic behavior of the exit probability of a L\'evy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are…
For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical Levy probability metric, given any number of atoms,…
We estimate the number of integer solutions to decomposable form inequalities (both asymptotic estimates and upper bounds are provided) when the degree of the form and the number of variables are relatively prime. These estimates display…
We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on the general setting of finite translation-invariant metric…
By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which…
The Learning Parity with Noise (LPN) problem underlines several classic cryptographic primitives. Researchers have attempted to demonstrate the algorithmic hardness of this problem by finding reductions from the decoding problem of linear…
Asymptotics for Dickman's number theoretic function $\rho(u)$, as $u \rightarrow \infty$, were given de Bruijn and Alladi, and later in sharper form by Hildebrand and Tenenbaum. The perspective in these works is that of analytic number…
This paper considers magnitude, asymptotics and duration of drawdowns for some L\'{e}vy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative L\'{e}vy processes using an approximation…
We derive asymptotic information on the iterates of a Volterra convolution operator acting on L^p(0,1), subject to a mild smoothness condition on the kernel. In particular, an asymptotically equal sequence of rank 1 operators is obtained,…
Let $X(t)$, $t\geq0$, be a L\'evy process in $\mathbb{R}^d$ starting at the origin. We study the closed convex hull $Z_s$ of $\{X(t): 0\leq t\leq s\}$. In particular, we provide conditions for the integrability of the intrinsic volumes of…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
An obvious way to simulate a L\'evy process $X$ is to sample its increments over time $1/n$, thus constructing an approximating random walk $X^{(n)}$. This paper considers the error of such approximation after the two-sided reflection map…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
In this paper we study the Assouad dimension of graphs of certain L\'evy processes and functions defined by stochastic integrals. We do this by introducing a convenient condition which guarantees a graph to have full Assouad dimension and…
IntLevPy provides a comprehensive description of the IntLevPy Package, a Python library designed for simulating and analyzing intermittent and L\'evy processes. The package includes functionalities for process simulation, including full…