Corpus ID: 237303855

Weak solutions to gamma-driven stochastic differential equations

@inproceedings{Belomestny2021WeakST,
  title={Weak solutions to gamma-driven stochastic differential equations},
  author={Denis Belomestny and Shota Gugushvili and Moritz Schauer and Peter Spreij},
  year={2021}
}
We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between the laws of solutions with different volatility functions. 
Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori asExpand

References

SHOWING 1-10 OF 18 REFERENCES
Stochastic integration and differential equations
I Preliminaries.- II Semimartingales and Stochastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Stochastic Integration and Local Times.- V Stochastic DifferentialExpand
Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori asExpand
Fluctuations of Lévy Processes with Applications: Introductory Lectures
Levy Processes and Applications.- The Levy-Ito Decomposition and Path Structure.- More Distributional and Path-Related Properties.- General Storage Models and Paths of Bounded Variation.-Expand
Risk Theory with the Gamma Process
The aggregate claims process is modelled by a process with independent, stationary and nonnegative increments. Such a process is either compound Poisson or else a process with an infinite number ofExpand
Limit Theorems for Stochastic Processes
I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale ProblemsExpand
A reliability model based on the gamma process and its analytic theory
This paper presents a variation of a state-dependent reliability model first proposed in Lemoine and Wenocur [4], [5], and develops some of its corresponding analytical theory. In particular, weExpand
Fluctuations of Lévy Processes with Applications
Algebra and Famous Inpossibilities Differential Systems Dumortier.: Qualitative Theory of Planar Jost, J.: Dynamical Systems. Examples of Complex Behaviour Jost, J.: Postmodern Analysis Jost, J.:Expand
Sur l'intégrabilité uniforme des martingales exponentielles
SommaireNous donnons des conditions suffisantes pour que la martingale localeℰ (M) définie par C. Doléans-Dade soit une martingale uniformément intégrable. Le lien est établi avec la martingaleExpand
Pricing an Option on Revenue from an Innovation: An Application to Movie Box Office Revenue
TLDR
A model for valuing revenue streams from innovations and the econometric methodology for ex ante parameter estimation and a Bayesian updating scheme using Markov chain Monte Carlo simulation as data after release become available are developed. Expand
Power-law behaviour and parametric models for the size-distribution of forest fires
This paper examines the distribution of areas burned in forest fires. Empirical size distributions, derived from extensive fire records, for six regions in North America are presented. While theyExpand
...
1
2
...