相关论文: Efficient evaluation of expectations of functions …
This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly…
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
Given a stable L\'{e}vy process $X=(X_t)_{0\le t\le T}$ of index $\alpha\in(1,2)$ with no negative jumps, and letting $S_t=\sup_{0\le s\le t}X_s$ denote its running supremum for $t\in [0,T]$, we consider the optimal prediction problem…
The distributed computing analysis of the accuracy of automodel solutions for the Green's function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have…
The controlled branching process is a generalization of the classical Bienaym\'e-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…
This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…
We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at $T$) of any L\'evy process on $[0,T]$ as $T\to\infty$.…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
We establish the functional convex order results for two scaled McKean-Vlasov processes $X=(X_{t})_{t\in[0, T]}$ and $Y=(Y_{t})_{t\in[0, T]}$ defined on a filtered probability space $(\Omega, \mathcal{F}, (\mathcal{F}_{t})_{t\geq0},…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We introduce a general algorithm for the computation of the scale functions of a spectrally negative L\'evy process $X$, based on a natural weak approximation of $X$ via upwards skip-free continuous-time Markov chains with stationary…
During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood…
The probability density function (PDF) of flux $R$ is computed in systems with logarithmic non-linearity using a model non-linear dynamical equation. The PDF tails of the first moment flux are analytically predicted to be power law. These…
We give upper and lower estimates of densities of convolution semigroups of probability measures under explicit assumptions on the corresponding Levy measure and the Levy--Khinchin exponent. We obtain also estimates of derivatives of…
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
A new method based on the maximum entropy principle for reconstructing the parton distribution function (PDF) from moments is proposed. Unlike traditional methods, the new method no longer needs to introduce any artificial assumptions. For…