Related papers: Local time penalizations with various clocks for o…
We study the penalization problem with various clocks where the weight is given as the exponential functional of multi-point local times for one-dimensional L\'{e}vy processes. The limit processes may vary according to the choice of random…
Several long-time limit theorems of one-dimensional L\'{e}vy processes weighted and normalized by functions of the local time are studied. The long-time limits are taken via certain families of random times, called clocks: exponential…
Long-time limit of one-dimensional L\'{e}vy processes weighted and normalized with respect to the exponential functional of two-point local times are studied. The limit processes may vary according to the choice of random clocks.
Several long-time limit theorems of one-dimensional L\'evy processes weighted and normalized by functions of its supremum are studied. The long-time limits are taken via the families of exponential times and that of constant times, called…
We present some limit theorems for the normalized laws (with respect to functionals involving last passage times at a given level up to time t) of a large class of null recurrent diffusions. Our results rely on hypotheses on the L\'evy…
We consider Brox's model: a one-dimensional diffusion in a Brownian potential W. We show that the normalized local time process (L(t;m_(log t) + x)=t; x \in R), where m_(log t) is the bottom of the deepest valley reached by the process…
Limit theorems for the normalized laws with respect to two kinds of weight functionals are studied for any symmetric stable L\'evy process of index $ 1 < \alpha \le 2 $. The first kind is a function of the local time at the origin, and the…
For a recurrent linear diffusion on $\R_+$ we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the L\'evy measure of the inverse local time is subexponential…
The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we…
We provide a brief discussion regarding relativistic limits on the discretization and temporal resolution of time values in a quantum clock. Our clock is characterized by a time observable chosen to be the complement of a bounded and…
For a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, we study the joint distribution of the two local times $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ and $B(t)= \int_{0}^{t} d\tau \delta(X(\tau)-L) $ at…
We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler…
We consider a symmetric random walk on the $\nu$-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction…
In this paper, we investigate the construction of a diffusion process whose time-marginal densities are constrained to belong to a given set at all time. The construction is obtained from a penalization approximation to the constraint set,…
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
We propose a discrete analogue for the boundary local time of reflected diffusions in bounded Lipschitz domains. This discrete analogue, called the discrete local time, can be effectively simulated in practice and is obtained pathwise from…
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…
The paper studies discrete time processes and their predictability and randomness in deterministic pathwise setting, without using probabilistic assumptions on the ensemble. We suggest some approaches to quantification of randomness based…
In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…