Related papers: Levy processes in cones of fuzzy vectors
The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle…
In this paper, we derive a Chen-Strichartz formula for stochastic differential equations driven by Levy processes, that is, we derive a series expansion of the logarithm of the flowmap of the stochastic differential equation in terms of…
We study monotone and convex stochastic orders for processes with independent increments. Our contributions are twofold: First, we relate stochastic orders of the Poisson component to orders of their (generalized) L\'evy measures. The…
When is it possible to interpret a given Markov process as a L\'evy-like process? Since the class of L\'evy processes can be defined by the relation between transition probabilities and convolutions, the answer to this question lies in the…
In this paper, we study some optimization problems in uniformly convex and uniformly smooth Bochner spaces. We consider four cases of the underlying subsets: closed and convex subsets, closed and convex cones, closed subspaces and closed…
We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random…
In this article we study the fractal Navier-Stokes equations by using stochastic Lagrangian particle path approach in Constantin and Iyer \cite{Co-Iy}. More precisely, a stochastic representation for the fractal Navier-Stokes equations is…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets…
Piecewise linear vector optimization problems in a locally convex Hausdorff topological vector spaces setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed…
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…
Given a set of $n$ points $P$ in the plane, the first layer $L_1$ of $P$ is formed by the points that appear on $P$'s convex hull. In general, a point belongs to layer $L_i$, if it lies on the convex hull of the set $P \setminus…
We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…
Since the presence of chaos in Bose-Einstein condensate (BEC) systems plays a destructive role that can undermine the stability of the condensates, controlling the chaos is of great importance for the creation of the BEC. In this paper, a…
We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under…
We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's…
Many engineering optimization problems can be considered as linear programming problems where all or some of the parameters involved are linguistic in nature. These can only be quantified using fuzzy sets. The aim of this paper is to solve…
In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definition which is a simple straightforward…
When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…
We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to two simpler problems. These Cauchy sub-problems respectively…