Related papers: Dilatively semistable stochastic processes
We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes…
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
In this paper we study pseudo-processes related to odd-order heat-type equations composed with L\'evy stable subordinators. The aim of the article is twofold. We first show that the pseudo-density of the subordinated pseudo-process can be…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…
In this work, we present a comprehensive theory of stochastic integration with respect to arbitrary cylindrical L\'evy processes in Hilbert spaces. Since cylindrical L\'evy processes do not enjoy a semi-martingale decomposition, our…
We construct two kinds of stochastic flows of discrete Galton-Watson branching processes. Some scaling limit theorems for the flows are proved, which lead to local and nonlocal branching superprocesses over the positive half line.
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
We prove a Poisson process approximation result for stabilizing functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
Stable distributions are a celebrated class of probability laws used in various fields. The $\alpha$-stable process, and its exponentially tempered counterpart, the Classical Tempered Stable (CTS) process, are also prominent examples of…
The aim of this short note is to present the notion of IDT processes, which is a wide generalization of L\'{e}vy processes obtained from a modified infinitely divisible property. Special attention is put on a number of examples, in order to…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…
We consider a functional semilinear Rayleigh-Stokes equation involving fractional derivative. Our aim is to analyze some circumstances, in those the global solvability and some results on asymptotic behavior of solutions take place. By…
We develop an asymptotic theory for the jump robust measurement of covariations in the context of stochastic evolution equation in infinite dimensions. Namely, we identify scaling limits for realized covariations of solution processes with…