Related papers: On the small-time behavior of subordinators

For a strictly stationary sequence of random vectors in $\mathbb{R}^d$ we study convergence of partial sum processes to L\'evy stable process in the Skorohod space with $J_1$-topology. We identify necessary and sufficient conditions for…

The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and…

The classical theorems about singular perturbation reduction (due to Tikhonov and Fenichel) are concerned with convergence on a compact time interval (in slow time) as a small parameter approaches zero. For unbounded time intervals…

We consider a large class of piecewise expanding maps T of [0,1] with a neutral fixed point, and their associated Markov chain Y_i whose transition kernel is the Perron-Frobenius operator of T with respect to the absolutely continuous…

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…

Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…

We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Furthermore, we present lower and upper bounds for the density.…

Let \begin{equation*} S_{0}=0,\quad S_{n}=X_{1}+...+X_{n},\ n\geq 1, \end{equation*} be a random walk whose increments belong without centering to the domain of attraction of a stable law with scaling constants $a_{n}$, that provide…

In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element…

The improper stochastic integral $Z=\int_0^{\infty-}\exp(-X_{s-})dY_s$ is studied, where $\{(X_t, Y_t), t \geqslant 0 \}$ is a L\'evy process on $\mathbb R ^{1+d}$ with $\{X_t \}$ and $\{Y_t \}$ being $\mathbb R$-valued and $\mathbb R…

Let $X=\{X_{t},t\in R_{+}\}$ be a symmetric L\'{e}vy process with local time $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$. When the L\'{e}vy exponent $\psi(\la)$ is regularly varying at zero with index $1<\beta\leq 2$, and satisfies…

We develop at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a class of asset-price models whose log returns follow a L\'evy process. Under mild assumptions placing the driving L\'evy process in…

In this note we look into detail at the box-counting dimension of subordinators. Given that $X$ is a non-decreasing Levy process, which is not a compound Poisson process, we show that in the limit, the minimum number of boxes of size…

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of…

In this paper, we consider transient subordinate Brownian motion X in R^d, d \geq 1, where the Laplace exponent \phi of the corresponding subordinator satisfies some mild conditions. The scaleinvariant Harnack inequality is proved for X. We…

In this paper, the weak convergence of additive functionals of processes with locally independent increments and with Markov switching in the scheme of Poisson approximation is proved. For the relative compactness, a method proposed by R.…

We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…

We revisit, in an original and challenging perspective, the problem of testing the null hypothesis that the mode of a directional signal is equal to a given value. Motivated by a real data example where the signal is weak, we consider this…

In this paper we prove a criterion of convergence in distribution in Skorokhod space. We apply this criterion to some special Levy processes and obtain almost-sure versions of limit theorems for these processes.

Let $L:\mathbb R\times \mathbb R\to [0, +\infty[\,\cup\{+\infty\}$ be a Borel function. We consider the problem \begin{equation}\tag{P}\min F(y)=\int_0^1L(y(t), y'(t))\,dt: y(0)=0,\, y\in W^{1,1}([0,1],\mathbb R).\end{equation} We give an…