The stochastic delay di erential equation dX (t) = ∫ [−r;0] X (t + u) a(du) dt + dZ(t); t¿0 is considered, where Z(t) is a process with independent stationary increments and a is a nite signed measure. We obtain necessary and su cient conditions for the existence of a stationary solution to this equation in terms of a and the L evy measure of Z . c © 2000 Elsevier Science B.V. All rights reserved.

We dispense with semimartingale (and Dirichlet process) assumptions while investigating arbitrary-order stochastic semi-linear parabolic equations. The emergence of fractional L evy processes in pressing applications like communication networks and mathematical nance highlights the need for studying stochastic evolutionary equations under general noise conditions. Our principle result states th...

We consider stochastic differential equations driven by a general L\'evy processes (SDEs) with infinite activity and the related, via Feynman-Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). approximate solution of PIDE using numerical method SDEs. The is based on three ingredients: (i) we small jumps diffusion; (ii) use restricted jump-adaptive time-stepping; ...

We dispense with semimartingale (and Dirichlet process) assumptions while investigating arbitrary-order stochastic semi-linear parabolic equations. The emergence of fractional L evy processes in pressing applications like communication networks and mathematical nance highlights the need for studying stochastic evolutionary equations under general noise conditions. Our principle result states th...

We consider the use of power law distributions P (x) j x j ?1? (1 < 2) for lattice gas automata (LGA). (a) We implement the distribution P (`) for particle displacements with length j ` j in a LGA and we investigate the resulting diiusive transport. We show that anomalous diiusion (var(j ` j) t 2==) cannot be observed, but that normal diiusion (h` 2 i Dt) can be tuned so that the diiusion coeec...

We present a general framework for the estimation of corporate default based on firm's capital structure, when its assets are assumed to follow pure jump L\'evy processes; this setup provides natural extension usual metrics defined in diffusion (log-normal) models, and allows capture extreme market events such as sudden drops asset prices, which closely linked occurrence. Within framework, we i...

We show that subexponentiality is not suucient to guarantee that the distribution tail of a sample quantile of an innnitely divisible process is equivalent to the \tail" of the same sample quantile under the corresponding L evy measure. However, such an equivalence result is shown to hold under either an assumption of an appropriatly slow tail decay or an assumption on the structure of the proc...

Jialun Zhou ([email protected]) Thira Sirisanthana ([email protected]) Sasisopin Kiertiburanakul ([email protected]) Yi-Ming A Chen ([email protected]) Ning Han ([email protected]) Poh_Lian Lim ([email protected]) Nagalingeswaran Kumarasamy ([email protected]) Jun Yong Choi ([email protected]) Tuti Parwati Merati ([email protected]) Evy Yunihastuti ([email protected])...

We introduce a type assignment system which is parametric with respect to ve families of trees obtained by evaluating -terms (Bohm trees, L evy-Longo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by the corresponding tree representation of terms. More precisely, for each family of trees, two terms...

Let U (n) denote the most visited point by a simple symmetric random walk fS k g k0 in the rst n steps. It is known that U (n) and max 0kn S k satisfy the same law of the iterated logarithm, but have diierent upper functions (in the sense of P. L evy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The correspo...