相关论文: L\'evy processes with partially stochastic resetti…
In this paper, we first show the well-posedness of the SDEs driven by L\'{e}vy noises under mild conditions. Then, we consider the existence and uniqueness of periodic solutions of the SDEs. To establish the ergodicity and uniqueness of…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…
Consider a random process s solution of the stochastic partial differential equation Ls = w with L a homogeneous operator and w a multidimensional L\'evy white noise. In this paper, we study the asymptotic effect of zooming in or zooming…
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…
In this paper, we introduce branching processes in a L\'evy random environment. In order to define this class of processes, we study a particular class of non-negative stochastic differential equations driven by Brownian motions and Poisson…
We study the connection between PDEs and L\'{e}vy processes running with clocks given by time-changed Poisson processes with stochastic drifts. The random times we deal with are therefore given by time-changed Poissonian jumps related to…
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…
Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary…
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting…
We provide a novel expression of the scale function for a L\'evy processes with negative phase-type jumps. It is in terms of a certain transition rate matrix which is explicit up to a single positive number. A monotone iterative scheme for…
We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under…
While stochastic resetting (or total resetting) is less young and more established concept in stochastic processes, partial stochastic resetting (PSR) is a relatively new field. PSR means that, at random moments in time, a stochastic…
This paper deals with generalized backward doubly stochastic differential equations driven by a L\'evy process (GBDSDEL, in short). Under left or right continuous and linear growth conditions, we prove the existence of minimal (resp.…
In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical {\alpha}-stable L\'evy processes via modulation or amplitude equations. We study SPDEs with a cubic…
This article studies the dynamics of a nonlinear dissipative reaction-diffusion equation with well-separated stable states which is perturbed by infinite-dimensional multiplicative L\'evy noise with a regularly varying component at…
We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general L\'evy…
We consider solutions of L\'evy-driven stochastic differential equations of the form $\mathrm{d} X_t=\sigma(X_{t-})\mathrm{d} L_t$, $X_0=x$ where the function $\sigma$ is twice continuously differentiable and maximal of linear growth and…
Recent developments on financial markets have revealed the limits of Brownian motion pricing models when they are applied to actual markets. L\'evy processes, that admit jumps over time, have been found more useful for applications. Thus,…