Related papers: Shot noise distributions and selfdecomposability
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
The low-frequency shot-noise power of a normal-metal-superconductor junction is studied for arbitrary normal region. Through a scattering approach, a formula is derived which expresses the shot-noise power in terms of the transmission…
A review is given of the shot-noise properties of metallic, diffusive conductors. The shot noise is one third of the Poisson noise, due to the bimodal distribution of transmission eigenvalues. The same result can be obtained from a…
We investigate weak convergence of renewal shot noise processes in the case of slowly varying tails of the inter-shot times. We show that these processes, after an appropriate non-linear scaling, converge in the sense of finite-dimensional…
1/f noise, the major source of dephasing in Josephson qubits, may be produced by an ensemble of two-level systems. Depending on the statistical properties of their distribution, the noise distribution can be Gaussian or non-Gaussian. The…
Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern…
The fluctuation in electric current in nonequilibrium steady states is investigated by molecular dynamics simulation of macroscopically uniform conductors. At low frequencies, appropriate decomposition of the spectral intensity of current…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…
We consider the maximum process of a random walk with additive independent noise in form of $\max_{i=1,\dots,n}(S_i+Y_i)$. The random walk may have dependent increments, but its sample path is assumed to converge weakly to a fractional…
Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle…
We investigate current fluctuations in non-degenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. We present an exact solution of the non-linear kinetic equations in the regime of…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
A spatially distributed system contains a large amount of agents with limited sensing, data processing, and communication capabilities. Recent technological advances have opened up possibilities to deploy spatially distributed systems for…
A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable…
Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…
The ever-growing appearance of infinitely divisible laws and related processes in various areas, such as physics, mathematical biology, finance and economics, has fuelled an increasing demand for numerical methods of sampling and sample…
This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…
We analyze the strong noise limit of one-dimensional stochastic differential equations (SDEs). Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an…
Optically levitated nanoparticles are promising candidates for the generation of macroscopic quantum states of mechanical motion. Protocols to generate such states expose the particle to a succession of different potentials. Limited…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…