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Найдено 12 публикаций
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Статья
Belomestny D., Panov V. Stochastic Processes and their Applications. 2013. Vol. 123. No. 1. P. 15-44.

In this paper, we prove a kind of Abelian theorem for a class of stochastic volatility models \((X,V),\) where both the state  process \(X\) and the volatility process \(V\) may have jumps. Our results  relate  the asymptotic behavior of the characteristic function of \(X_{\Delta}\) for some \(\Delta>0\) in a stationary regime to the Blumenthal-Getoor indexes of the  L\'evy processes driving the jumps in \(X\) and \(V\). The results obtained are used to construct consistent estimators for the above Blumenthal-Getoor indexes  based on low-frequency observations of the state process \(X\). We derive the convergence rates for the corresponding estimator and show that these rates can not be improved in general. 

Добавлено: 23 сентября 2013
Статья
L.Huang, Frikha N. Stochastic Processes and their Applications. 2015. No. 125. P. 4066-4101.
Добавлено: 14 октября 2015
Статья
Decrouez G. G., Braunsteins P., Hautphenne S. Stochastic Processes and their Applications. 2018.
Добавлено: 22 марта 2018
Статья
Jabir J. M., Profeta C. Stochastic Processes and their Applications. 2019. Vol. 129. No. 11. P. 4269-4293.
Добавлено: 15 ноября 2019
Статья
Lefevere R., Mariani M., Zambotti L. Stochastic Processes and their Applications. 2011. Vol. 121. No. 10. P. 2243-2271.
Добавлено: 8 октября 2018
Статья
Menozzi S. Stochastic Processes and their Applications. 2018. Vol. 128. P. 756-802.
Добавлено: 3 декабря 2018
Статья
Veretennikov A., Butkovsky O. Stochastic Processes and their Applications. 2013. Vol. 123. No. 9. P. 3518-3541.
Добавлено: 18 октября 2014
Статья
Gushchin A. A., Küchler U. Stochastic Processes and their Applications. 2000. Vol. 88. No. 2. P. 195-211.

Let a be a finite signed measure on [-r,0], Z a Lévy process (that is a real process with independent stationary increments and càdlàg paths). A linear stochastic delay differential equation

X(t)=X(0)+∫ 0 t ∫ [-r,0] X(s+u)da(u)ds+Z(t),t≥0,(1)

driven by Z is studied, only càdlàg solutions to (1) such that Z and (X(t),-r≤t≤0) are independent being considered. Set h(λ)=λ-∫ [-r,0] exp(λu)da(u) and v 0 =sup{Reλ∣λ∈ℂ,h(λ)=0}. Let the Lévy measure of jumps of the process Z be denoted by F. It is shown that there exists a stationary solution to (1) if and only if v 0 <0 and ∫ |y|>1 log|y|dF(y)<∞. If X is a stationary solution to (1), then X(t) equals in law to ∫ 0 ∞ x 0 (t)dZ(t), where x 0 is the fundamental solution of the deterministic counterpart (Z≡0) to (1).

Добавлено: 8 октября 2013
Статья
Belomestny D., Schoenmakers J. Stochastic Processes and their Applications. 2016. Vol. 126. No. 7. P. 2092-2122.

Given a Lévy process (Lt)t≥0 and an independent nondecreasing process (time change) (T(t))t≥0, we consider the problem of statistical inference on T based on low-frequency observations of the time-changed Lévy process LT(t). Our approach is based on the genuine use of Mellin and Laplace transforms. We propose a consistent estimator for the density of the increments of T in a stationary regime, derive its convergence rates and prove the optimality of the rates. It turns out that the convergence rates heavily depend on the decay of the Mellin transform of T. Finally, the performance of the estimator is analysed via a Monte Carlo simulation study.

 

Добавлено: 4 мая 2016
Статья
Decrouez G. G., Hambly B., Jones O. D. Stochastic Processes and their Applications. 2015.
Добавлено: 12 января 2015
Статья
Moulines E., Brosse N., Durmus A. et al. Stochastic Processes and their Applications. 2018. P. 1-26.

In this article, we consider the problem of sampling from a probability measure π having a density on R d proportional to x↦ e− U (x). The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable, when the potential U is superlinear. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tamed Unadjusted Langevin Algorithm (TULA) and obtain non-asymptotic bounds in V-total variation norm and Wasserstein distance of order 2 between the iterates of TULA and π, as well as weak error bounds. Numerical experiments are presented which support our findings.

Добавлено: 11 декабря 2018
Статья
Kelbert M., Konakov V., Menozzi S. Stochastic Processes and their Applications. 2016. Vol. 126. P. 1145-1183.

We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential Equations (P(I)DEs). Namely, we consider equations involving a time fractional derivative of Caputo type and a spatial operator corresponding to the generator of a non degenerate Brownian or stable driven Stochastic Differential Equation (SDE).

Добавлено: 21 марта 2016