Related papers: Drawdowns of diffusions
A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed,…
A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with…
By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a…
We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…
Levy flights are random walks in which the probability distribution of the step sizes is fat-tailed. Levy spatial diffusion has been observed for a collection of ultra-cold Rb atoms and single Mg+ ions in an optical lattice. Using the…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence…
This article introduces two techniques for computing the distribution of the absorption or first passage time of the drifted Wiener diffusion subject to Poisson resetting times, to an upper hard wall barrier and to a lower absorbing…
Mathematical models of diffusive transport underpin our understanding of chemical, biochemical and biological transport phenomena. Analysis of such models often focusses on relatively simple geometries and deals with diffusion through…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…
This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated…
Recently, we provided a simple but accurate formula which closely approximates the first crossing distribution associated with random walks having correlated steps. The approximation is accurate for the wide range of barrier shapes of…
We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean…
We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…
In this work, we develop excursion theory for the Wright--Fisher diffusion with mutation. Our construction is intermediate between the classical excursion theory where all excursions begin and end at a single point and the more general…
This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the…
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…