Related papers: Multifractality of jump diffusion processes
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…
We define a large class of continuous time multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined…
Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
In this paper, we investigate periodic solutions of regime-switching jump diffusions. We first show the well-posedness of solutions to the SDEs corresponding to the hybrid system. Then, we derive the strong Feller property and…
The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
We establish a local martingale $M$ associate with $f(X,Y)$ under some restrictions on $f$, where $Y$ is a process of bounded variation (on compact intervals) and either $X$ is a jump diffusion (a special case being a L\'evy process) or $X$…
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…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
The paper discusses multivariate self- and cross-exciting processes. We define a class of multivariate point processes via their corresponding stochastic intensity processes that are driven by stochastic jumps. Essentially, there is a jump…
We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
We consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial…