Related papers: A Multiplier Related to Symmetric Stable Processes

Let $V$ be a two sided random walk and let $X$ denote a real valued diffusion process with generator ${1/2}e^{V([x])}\frac{d}{dx}(e^{-V([x])}\frac{d}{dx})$. This process is known to be the continuous equivalent of the one dimensional random…

The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…

This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these…

This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a…

In the recent article D\"oring et al. [4] the authors conditioned a stable process with two-sided jumps to avoid an interval. As usual the strategy was to find an invariant function for the process killed on entering the interval and to…

In a recent work by A. Martini and A. Sikora (arXiv:1204.1159), sharp L^p spectral multiplier theorems for the Grushin operators acting on $R^{d_1} \times R^{d_2}$ are obtained in the case $d_1 \geq d_2$. Here we complete the picture by…

We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier.…

Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded noise gain is typically proven. In recent work it has been shown, in both the pole placement…

We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite…

We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…

Multipliers can be used to guarantee both the Lyapunov stability and input-output stability of Lurye systems with time-invariant memoryless slope-restricted nonlinearities. If a dynamic multiplier is used there is no guarantee the…

We consider an exploration algorithm where at each step, a random number of items become active while related items get explored. Given an initial number of items $N$ growing to infinity and building on a strong homogeneity assumption, we…

Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…

We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a Wiener process) multiplied by a possibly degenerate…

Replacing the spectral measure by a random vector $\bfZ$ allows the representation of a max-stable distribution on $\R^d$ with standard negative margins via a norm, called \emph{$D$-norm}, whose generator is $\bfZ$. The set of $D$-norms can…

The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…

The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…

We obtain an asymptotic H\"older estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the…

When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…

In this paper, we consider a linear model with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its intensity are unknown parameters. Supposing that the process is…