Related papers: Rejection Sampling for Tempered Levy Processes
We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Levy processes. From this we introduce a general method for generating new families of scale functions. Using this method we…
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered…
In this article we consider the Levy processes and the corresponding semigroup. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization…
We provide series expansions for the tempered stable densities and for the price of European-style contracts in the exponential L\'evy model driven by the tempered stable process. These formulas recover several popular option pricing…
We study the nonparametric estimation of the jump density of a renewal reward process from one discretely observed sample path over [0,T]. We consider the regime when the sampling rate goes to 0. The main difficulty is that a renewal reward…
In this paper we develop a new general Bayesian methodology that simultaneously estimates parameters of interest and the marginal likelihood of the model. The proposed methodology builds on Simulated Tempering, which is a powerful algorithm…
Large language models (LLMs) have made impressive strides in mathematical reasoning, often fine-tuned using rejection sampling that retains only correct reasoning trajectories. While effective, this paradigm treats supervision as a binary…
The simulation of rare events is one of the key problems in atomistic simulations. Towards its solution a plethora of methods have been proposed. Here we combine two such methods metadynamics and inte-grated tempering sampling. In…
We present a mechanism to steer the sampling diversity of denoising diffusion and flow matching models, allowing users to sample from a sharper or broader distribution than the training distribution. We build on the observation that these…
Rejection sampling is a common tool for low dimensional problems ($d \leq 2$), often touted as an "easy" way to obtain valid samples from a distribution $f(\cdot)$ of interest. In practice it is non-trivial to apply, often requiring…
In this paper we propose an acceptance-rejection sampler using stratified inputs as diver sequence. We estimate the discrepancy of the points generated by this algorithm. First we show an upper bound on the star discrepancy of order…
This paper deals with the large deviations behavior of a stochastic process called thinned Levy process. This process appeared recently as a stochastic-process limit in the context of critical inhomogeneous random graphs. The process has a…
We investigate a refracted Levy process driven by a jump diffusion process, whose jumps have rational Laplace transforms. For such a stochastic process, formulas for the Laplace transform of its occupation times are deduced. To derive the…
We completely describe the size and large intersection properties of the Holder singularity sets of Levy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a Levy process. The Holder…
Speculative sampling (SpS) has been successful in accelerating the decoding throughput of auto-regressive large language models by leveraging smaller draft models. SpS strictly enforces the generated distribution to match that of the…
We demonstrate that the method of interleaved resampling in the context of parton showers can tremendously improve the statistical convergence of weighted parton shower evolution algorithms. We illustrate this by several examples showing…
We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in $\alpha$-stable $(1< \alpha \le 2)$ i.i.d. innovations and related tempered linear processes with vanishing tempering parameter $\lambda…
In the paper [Hainaut, D. and Colwell, D.B., {\rm A structural model for credit risk with switching processes and synchronous jumps}, The European Journal of Finance 22(11) (2016): 1040-1062], the authors exploit a synchronous-jump…