Short-time large deviations of first-passage functionals for high-order stochastic processes

Abstract

We consider high-order stochastic processes $x(t)$ described by the Langevin equation $\frac{d^{m}x\left(t\right)}{d{t}^m}=\sqrt{2D}\xi (t)$, where $\xi (t)$ is a delta-correlated Gaussian noise with zero mean, and $D$ is the strength of noise. We focus on the short-time statistics of the first-passage functionals $A={\int }_0^T{\left[x(t)\right]}^{n}dt$ along the trajectories starting from $x(0)=L$ and terminating whenever passing through the origin for the first-time at $t=T$. Using the optimal fluctuation method, we analytically obtain the most likely realizations of the first-passage processes for a given constraint $A$ with $n=0$ and 1, corresponding to the first-passage time itself and the area swept by the first-passage trajectory, respectively. The tail of the distribution of $A$ shows an essential singularity at $A\to 0$, $P_{m,n}(A|L)\sim \exp \left(-\frac{{\alpha }_{m,n}{L}^{2mn-n+2}}{D{A}^{2m-1}}\right)$, where the explicit expressions for the exponents ${\alpha }_{m,0}$ and ${\alpha }_{m,1}$ for arbitrary $m$ are obtained.

11 pages, 3 figures

References in corpus (56)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Nontrivial Exponent for Simple Diffusion
• Exact Maximal Height Distribution of Fluctuating Interfaces
• Introduction to dynamical large deviations of Markov processes
• WKB theory of large deviations in stochastic populations
• The Local and the Occupation Time of a Particle Diffusing in a Random Medium
• From the area under the Bessel excursion to anomalous diffusion of cold atoms
• A minimal model of dynamical phase transition
• Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation
• Generalized arcsine laws for fractional Brownian motion
• On the area under a continuous time Brownian motion till its first-passage time
• Properties of additive functionals of Brownian motion with resetting
• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Dynamical phase transition in drifted Brownian motion
• Time to reach the maximum for a random acceleration process
• Anomalous scaling of dynamical large deviations
• Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential
• Extremal statistics for stochastic resetting systems
• Occupation time of a run-and-tumble particle with resetting
• Local time of diffusion with stochastic resetting
• The first-passage area for drifted Brownian motion and the moments of the Airy distribution
• Exact persistence exponent for the $2d$-diffusion equation and related Kac polynomials
• The Airy distribution: experiment, large deviations and additional statistics
• The convex hull for a random acceleration process in two dimensions
• Extreme value statistics and arcsine laws for heterogeneous diffusion processes
• Statistics of first-passage Brownian functionals
• Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process
• Persistence Exponents and the Statistics of Crossings and Occupation Times for Gaussian Stationary Processes
• Geometrical optics of constrained Brownian motion: three short stories
• Toward the full short-time statistics of an active Brownian particle on the plane
• Arcsine Laws in Stochastic Thermodynamics
• Anomalous scaling of dynamical large deviations of stationary Gaussian processes
• Residence time statistics for $N$ blinking quantum dots and other stochastic processes
• Local time for run and tumble particle
• Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Geometrical optics of large deviations of fractional Brownian motion
• Large fluctuations of the area under a constrained Brownian excursion
• On the joint distribution of first-passage time and first-passage area of drifted Brownian motion
• Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles
• First-passage functionals of Brownian motion in logarithmic potentials and heterogeneous diffusion
• Geometrical optics of first-passage functionals of random acceleration
• Extreme Value Statistics and Arcsine Laws of Brownian Motion in the Presence of a Permeable Barrier
• Local time of a system of Brownian particles on the line with steplike initial condition
• Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a $|x|$ potential
• Occupation time of a system of Brownian particles on the line with steplike initial condition
• Area fluctuations on a subinterval of Brownian excursion
• Macroscopic fluctuation theory of local time in lattice gases
• Large deviations in statistics of the local time and occupation time for a run and tumble particle
• First-passage area distribution and optimal fluctuations of fractional Brownian motion
• Extremal statistics for a one-dimensional Brownian motion with a reflective boundary
• Geometrical optics of large deviations of Brownian motion in inhomogeneous media
• Stiffness of random walks with reflecting boundary conditions
• Short-time large deviation of constrained random acceleration process