Competition between L ! evy jumps and continuous drift
نویسنده
چکیده
Motivated by certain birth–death processes with strongly "uctuating birth rates, we consider a level-crossing problem for a random process being a superposition of a continuous drift to the left and jumps to the right. The lengths of the corresponding jumps follow a one-sided extreme L! evy-law of index !. We concentrate on the case 0¡ !¡ 1 and discuss the probability of crossing a left boundary (“extinction”). We show that this probability decays exponentially as a function of the initial distance to the boundary. Such behavior is universal for all !¡ 1 and is exempli#ed by an exact solution for the special case != 2 . The splitting probabilities are also discussed. c © 2003 Elsevier B.V. All rights reserved. PACS: 05.40.+j; 02.50.−r
منابع مشابه
Asymptotic Distributions of the Continuous - TimeRandom
We provide a systematic analysis of the possible asymptotic distributions of one-dimensional continuous-time random walks (CTRWs) by applying the limit theorems of probability theory. Biased and unbiased walks of coupled and decoupled memory are considered. In contrast to previous works concerning decoupled memory and L evy walks, we deal also with arbitrary coupled memory and with jump densiti...
متن کاملL Evy-driven Continuous-time Arma Processes
Gaussian ARMA processes with continuous time parameter, otherwise known as stationary continuous-time Gaussian processes with rational spectral density , have been of interest for many years. In the last twenty years there has been a resurgence of interest in continuous-time processes, partly as a result of the very successful application of stochastic diierential equation models to problems in...
متن کاملOptimal Stopping and Perpetual Options for L Evy Processes Optimal Stopping and Perpetual Options for L Evy Processes
Solution to the optimal stopping problem for a L evy process and reward functions (e x ?K) + and (K ?e x) + , discounted at a constant rate is given in terms of the distribution of the overall supremum and innmum of the process killed at this rate. Closed forms of this solutions are obtained under the condition of positive jumps mixed-exponentially distributed. Results are interpreted as admiss...
متن کاملEvy - Driven and Fractionally Integrated Armaprocesses with Continuous Time Parameterpeter
The deenition and properties of L evy-driven CARMA (continuous-time ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion. The use of more general L evy processes permits the speciication of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus-sian. Non-negative...
متن کاملEvy Driven and Fractionally Integrated Arma Processes with Continuous Time Parameter
The de nition and properties of L evy driven CARMA continuous time ARMA processes are re viewed Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion The use of more general L evy processes permits the speci cation of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus sian Non negative CAR...
متن کامل