Finite dimensional characteristic functions of Brownian rough path

2017 ◽  
Vol 12 (4) ◽  
pp. 859-877
Author(s):  
Xi Geng ◽  
Zhongmin Qian
Keyword(s):  
Characteristic Functions ◽  
Finite Dimensional ◽  
Dimensional Characteristic ◽  
Rough Path

QUASI-SURE EXISTENCE OF BROWNIAN ROUGH PATHS AND A CONSTRUCTION OF BROWNIAN PANTS

2006 ◽  
Vol 09 (04) ◽  
pp. 513-528 ◽  
Author(s):  
YUZURU INAHAMA
Keyword(s):  
Loop Space ◽  
Compact Manifold ◽  
Continuous Process ◽  
Rough Paths ◽  
Finite Dimensional ◽  
Rough Path

In this paper we will prove the quasi-sure existence of the Brownian rough path for finite-dimensional cases. As an application we will give a construction of Brownian pants, that is a certain continuous process on the continuous loop space over a compact manifold.

scholarly journals SUPERSYMMETRY OF PARAFERMIONS

1999 ◽  
Vol 14 (39) ◽  
pp. 2739-2752 ◽  
Author(s):  
SERGEI KLISHEVICH ◽  
MIKHAIL PLYUSHCHAY
Keyword(s):  
Single Mode ◽  
Type Systems ◽  
Characteristic Functions ◽  
Finite Dimensional ◽  
Deformed Oscillator

We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The supersymmetry is realized in both unbroken and spontaneously broken phases. As in the case of parabosonic supersymmetry observed recently by one of the authors, the form of the associated superalgebra depends on the order of the parafermion and can be linear or nonlinear in the Hamiltonian. The list of supersymmetric parafermionic systems includes usual parafermions, finite-dimensional q-deformed oscillator, q-deformed parafermionic oscillator and parafermionic oscillator with internal Z2 structure.

scholarly journals On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations

2021 ◽  
Vol 71 (5) ◽  
pp. 1241-1268
Author(s):  
Mátyás Barczy ◽  
Fanni K. Nedényi ◽  
Gyula Pap
Keyword(s):  
Density Function ◽  
Explicit Formula ◽  
Time Scale ◽  
Random Coefficient ◽  
Partial Sums ◽  
Characteristic Functions ◽  
Autoregressive Processes ◽  
Finite Dimensional ◽  
Joint Characteristic

Abstract We investigate joint temporal and contemporaneous aggregation of N independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient α ∈ (0, 1) and with idiosyncratic Poisson innovations. Assuming that α has a density function of the form ψ(x) (1 − x) β , x ∈ (0, 1), with β ∈ (−1, ∞) and lim x ↑ 1 ψ ( x ) = ψ 1 ∈ ( 0 , ∞ ) $\lim\limits_{x\uparrow 1} \psi(x) = \psi_1 \in (0, \infty)$ , different limits of appropriately centered and scaled aggregated partial sums are shown to exist for β ∈ (−1, 0] in the so-called simultaneous case, i.e., when both N and the time scale n increase to infinity at a given rate. The case β ∈ (0, ∞) remains open. We also give a new explicit formula for the joint characteristic functions of finite dimensional distributions of the appropriately centered aggregated process in question.

scholarly journals ANOTHER APPROACH TO SOME ROUGH AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 535-550 ◽  
Author(s):  
JOSEF TEICHMANN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Solution Process ◽  
Partial Differential ◽  
State Spaces ◽  
New Approach ◽  
Finite Dimensional ◽  
Rough Path ◽  
Rough Path Theory

In this paper, we introduce a new approach to rough and stochastic partial differential equations (RPDEs and SPDEs): we consider general Banach spaces as state spaces and — for the sake of simplicity — finite dimensional sources of noise, either rough or stochastic. By means of a time-dependent transformation of state space and rough path theory, we are able to construct unique solutions of the respective R- and SPDEs. As a consequence of our construction, we can apply the pool of results of rough path theory, in particular we can obtain strong and weak numerical schemes of high order converging to the solution process.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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