Related papers: L\'evy noise-driven escape from arctan potential w…
We consider the motion of an overdamped particle in a force field in presence of an external, adiabatic noise, without the restriction that the noise process is Gaussian or the stochastic process is Markovian. We examine the condition for…
We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the…
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…
We study the most probable trajectories of the concentration evolution for the transcription factor activator in a genetic regulation system, with non-Gaussian stable L\'evy noise in the synthesis reaction rate taking into account. We…
In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents.…
We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of L\'evy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D…
We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by…
We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its…
For spectrally negative L\'evy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…
We investigate the escape rate of an overdamped, self-propelled spherical Brownian particle on a surface from a metastable potential well. Within a modeling in terms of a 1D constant speed of the particle's active dynamics we consider the…
This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…
We study the speed of extinction of continuous state branching processes in a L\'evy environment, where the associated L\'evy process oscillates. Assuming that the L\'evy process satisfies the Spitzer's condition and the existence of some…
L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an…
Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by L\'{e}vy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive…
We study the effects of noise-intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions,…
For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. Using Malliavin calculus tools, we obtain precise vanishing noise asymptotics for the tail…
It is a common phenomenon in nature and technology that a system under perturbations exits a regime of its usual dynamics. Often it is possible to define a potential function whereby a potential well can be associated with a usual or…
We consider the exit event from a metastable state for the overdamped Langevin dynamics $dX_t = -\nabla f(X_t) dt + \sqrt{h} dB_t$. Using tools from semiclassical analysis, we prove that, starting from the quasi stationary distribution…
We present a study of the noise driven escape of an overdamped Brownian particle moving in a cubic potential profile with a metastable state. We analyze the role of the initial conditions of the particle on the enhancement of the average…