Related papers: Transition density estimates for jump L\'evy proce…
For a broad class of the Levy processes the new form (convolution type) of the infinitesimal generators is introduced. It leads to the new notions: a truncated generator, a quasi-potential. The probability of the Levy process remaining…
The problem of estimating the L\'evy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the…
Via a Bismut-Elworthy-Li formula from [KPP23], we derive uniform gradient estimates for transition semigroups associated with stochastic differential equations driven by a large class of cylindrical L\'{e}vy processes which includes the…
We consider a new method of the semiparametric statistical estimation for the continuous-time moving average L\'evy processes. We derive the convergence rates of the proposed estimators, and show that these rates are optimal in the minimax…
Let $X$ be a $d$-dimensional L\'evy process with L\'evy triplet $(\Sigma,\nu,\alpha)$ and $d\geq 2$. Given the low frequency observations $(X_t)_{t=1,\ldots,n}$, the dependence structure of the jumps of $X$ is estimated. The L\'evy measure…
We present an existence result for L\'evy-type processes which requires only weak regularity assumptions on the symbol $q(x,\xi)$ with respect to the space variable $x$. Applications range from existence and uniqueness results for…
The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for L\'evy type stochastic differential equation. In…
This work develops Feynman-Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated to a general L\'evy process and the switching part depends on the jump…
The master equation for a probability density function (pdf) driven by L\'{e}vy noise, if conditioned to conform with the principle of detailed balance, admits a transformation to a contractive strongly continuous semigroup dynamics. Given…
In this paper, we study transition density functions for pure jump unimodal L\'evy processes killed upon leaving an open set $D$. Under some mild assumptions on the L\'evy density, we establish two-sided Dirichlet heat kernel estimates when…
We propose a new method for the estimation of a semiparametric tempered stable L\'{e}vy model. The estimation procedure combines iteratively an approximate semiparametric method of moment estimator, Truncated Realized Quadratic Variations…
This paper gives examples of explicit arbitrage-free term structure models with L\'evy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a L\'evy process…
A compound Poisson process whose jump measure and intensity are unknown is observed at finitely many equispaced times. We construct a purely data-driven estimator of the L\'evy density $\nu$ through the spectral approach using general…
We consider Feller semigroups of operators determinated by systems of jumps dominated by the rotation invariant stable L\'evy measure. Using an approximation schema we prove the existence and obtain estimates of corresponding heat kernels.
We consider an Ornstein-Uhlenbeck process with values in R^n driven by a L\'evy process (Z_t) taking values in R^d with d possibly smaller than n. The L\'evy noise can have a degenerate or even vanishing Gaussian component. Under a…
Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate L\'evy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting…
Monotone L\'evy processes with additive increments are defined and studied. It is shown that these processes have a natural Markov structure and their Markov transition semigroups are characterized using the monotone L\'evy-Khintchine…
In this article we derive formula for probability $\Prob(\sup_{t\leq T} (X(t)-ct)>u)$ where $X=\{X(t)\}$ is a spectrally positive L\'evy process and $c\in\RL$. As an example we investigate the inverse Gaussian L\'evy process.
In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form $$Z_{t} = \int_{\mathbb{R}}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}$$ with a deterministic kernel (\K\) and a…
We consider SDEs driven by multiplicative pure jump L\'{e}vy noises, where L\'evy processes are not necessarily comparable to $\alpha$-stable-like processes. By assuming that the SDE has a unique solution, we obtain gradient estimates of…