相关论文: Levy Processes, Generators
This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in…
For a refracted L\'evy process driven by a spectrally negative L\'evy process, we use a different approach to derive expressions for its q-potential measures without killing. Unlike previous methods whose derivations depend on scale…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…
There is no known way of giving a domain-theoretic semantics to higher-order probabilistic languages, in such a way that the involved domains are continuous or quasi-continuous - the latter is required to do any serious mathematics. We…
We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also…
It is known that the exponential functional of a Poisson process admits a probability density function in the form of an infinite series. In this paper, we obtain an explicit expression for the density function of the exponential functional…
The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a…
We study the small-time asymptotics of sample paths of L\'evy processes and L\'evy-type processes. Namely, we investigate under which conditions the limit $$\limsup_{t \to 0} \frac{1}{f(t)} |X_t-X_0|$$ is finite resp.\ infinite with…
Relations between so-called harness processes and initial enlargements of the filtration of a Levy process with its positions at fixed times are investigated.
We consider natural exponential families of Levy processes with randomized parameter. Such processes are Markov, and under suitable assumptions, pairs of such processes with shared randomization can be stitched together into a single…
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
It is proved that the random integral mappings (some type of functionals of L\'evy processes) are always isomorphisms between convolution semigroups of infinitely divisible measures. However, the inverse mappings are no longer of the random…
In the work asymptotic analysis of the problem of large deviations for random evolutions with independent increments in the circuit of L\'{e}vy approximation is carried out. Large deviations for random evolutions in the circuit of Levy…
The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is…
We introduce a novel model called GAMMT (Generative Ambiguity Models using Multiple Transformers) for sequential data that is based on sets of probabilities. Unlike conventional models, our approach acknowledges that the data generation…
First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…
The present paper aims to demonstrate the usage of Convolutional Neural Networks as a generative model for stochastic processes, enabling researchers from a wide range of fields (such as quantitative finance and physics) to develop a…
What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of…
We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer coefficients. Consequently we can compute the L\'evy constant…
We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random…