Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEfficient almost-exact Levy area sampling
135
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a new method for sampling the Levy area for a two-dimensional Wiener process conditioned on its endpoints. An efficient sampler for the Levy area is required to implement a strong Milstein numerical scheme to approximate the solution of a stochastic differential equation driven by a two-dimensional Wiener process whose diffusion vector fields do not commute. Our method is simple and complementary to those of Gaines-Lyons and Wiktorsson, and amenable to quasi-Monte--Carlo implementation. It is based on representing the Levy area by an infinite weighted sum of independent Logistic random variables. We use Chebychev polynomials to approximate the inverse distribution function of sums of independent Logistic random variables in three characteristic regimes. The error is controlled by the degree of the polynomials, we set the error to be uniformly 10^(-12). We thus establish a strong almost-exact Levy area sampling method. The complexity of our method is square logarithmic. We indicate how our method can contribute to efficient sampling in higher dimensions.
rate research
Read More
A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of Levy driven stochastic integrals with deterministic kernels. Exact asymptotic behavior is established for (a) the transition probability density of a real-valued Levy process; (b) the transition probability density and the invariant distribution density of a Levy driven Ornstein-Uhlenbeck process; (c) the distribution density of the fractional Levy motion.
In this paper, we study almost periodic solutions for semilinear stochastic differential equations driven by L{e}vy noise with exponential dichotomy property. Under suitable conditions on the coefficients, we obtain the existence and uniqueness of bounded solutions. Furthermore, this unique bounded solution is almost periodic in distribution under slightly stronger conditions. We also give two examples to illustrate our results.
A recently developed semiclassical approximation to exchange in one dimension is shown to be almost exact, with essentially no computational cost. The variational stability of this approximation is tested, and its far greater accuracy relative to local density functional calculations demonstrated. Even a fully orbital-free potential-functional calculation (no orbitals of any kind) yields little error relative to exact exchange, for more than one orbital.
In this paper we address the problem of rare-event simulation for heavy-tailed Levy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for heavy-tailed Levy processes, stick-breaking approximation of extrema of Levy processes, and the randomized debiasing Monte Carlo scheme. The proposed importance sampling algorithm can be applied to a broad class of Levy processes and exhibits significant improvements in efficiency when compared to crude Monte-Carlo method in our numerical experiments.
In this paper we introduce a new class of state space models based on shot-noise simulation representations of non-Gaussian Levy-driven linear systems, represented as stochastic differential equations. In particular a conditionally Gaussian version of the models is proposed that is able to capture heavy-tailed non-Gaussianity while retaining tractability for inference procedures. We focus on a canonical class of such processes, the $alpha$-stable Levy processes, which retain important properties such as self-similarity and heavy-tails, while emphasizing that broader classes of non-Gaussian Levy processes may be handled by similar methodology. An important feature is that we are able to marginalise both the skewness and the scale parameters of these challenging models from posterior probability distributions. The models are posed in continuous time and so are able to deal with irregular data arrival times. Example modelling and inference procedures are provided using Rao-Blackwellised sequential Monte Carlo applied to a two-dimensional Langevin model, and this is tested on real exchange rate data.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
