Related papers: Stochastic integral representations and classifica…
A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability…
We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…
Recently, many classes of infinitely divisible distributions on R^d have been characterized in several ways. Among others, the first way is to use Levy measures, the second one is to use transformations of Levy measures, and the third one…
For a superprocess under a stochastic flow, we prove that it has a density with respect to the Lebesgue measure for d=1 and is singular for d>1. For d=1, a stochastic partial differential equation is derived for the density. The regularity…
The limiting behavior of stochastic evolution processes with small noise intensity $\epsilon$ is investigated in distribution-based approach. Let $\mu^{\epsilon}$ be stationary measure for stochastic process $X^{\epsilon}$ with small…
Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming…
In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…
We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…
Dilative semistability extends the notion of semi-selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. It is shown that this scaling relation is a natural extension…
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space $\Phi$. Our construction of the stochastic integral is based on the theory of tensor products…
Continuing the study reported in Satheesh (2001),(arXiv:math.PR/0304499 dated 01May2003) here we study certain aspects of randomization in infinitely divisible (ID) and max-infinitely divisible (MID) laws. They generalize ID and MID laws.…
The paper addresses the question whether a random functional, a map from a set $E$ into the space of real-valued measurable functions on a probability space, has a measurable version with values in ${\mathbb R}^E$. Similarly, one may ask…
The statistical linearization method known in nonlinear mechanics and random vibrations theory has been applied to stochastically quantized fields in finite temperature. It has been shown that even in its simplest form the method yields…