Related papers: Density estimates for jump diffusion processes
We study the blow up solutions of a semilinear reaction diffusion system coupled in both equations and boundary conditions. The main purpose is to understand how the reaction terms and the absorption terms affect the blow-up properties. We…
Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve diffusion process and its running maximum. Our approach is to use the excursion theory for Levy processes. Since general diffusions are, in…
We obtain two-sided bounds for the density of stochastic processes satisfying a weak H\"ormander condition. In particular we consider the cases when the support of the density is not the whole space and when the density has various…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…
As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts for the uncertain permeability of a given…
The filtering equations associated to a partially observed jump diffusion model $(Z_t)_{t\in [0,T]}=(X_t,Y_t)_{t\in [0,T]}$, driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
We prove maximum principles for the problem of optimal control for a jump diffusion with infinite horizon and partial information. The results are applied to partial information optimal consumption and portfolio problems in infinite…
Given a doubly infinite sequence of positive numbers {c_k: k in Z} satisfying a LLN with limit A, we consider the nearest-neighbor simple exclusion process on Z where c_k is the probability rate of jumps between k and k+1. If A is infinite…
This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further…
Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the…
We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin…
We study the low-energy solutions to the 3D compressible Navier-Stokes-Poisson equations. We first obtain the existence of smooth solutions with small $L^2$-norm and essentially bounded densities. No smallness assumption is imposed on the…
This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a…
We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…
Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to…
This paper is the third part of our study started with Cattiaux, Le\'{o}n and Prieur [Stochastic Process. Appl. 124 (2014) 1236-1260; ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 359-384]. For some ergodic Hamiltonian systems, we obtained…
The Langevin dynamics is a diffusion process extensively used, in particular in molecular dynamics simulations, to sample Gibbs measures. Some alternatives based on (piecewise deterministic) kinetic velocity jump processes have gained…