TITLE

Topological field theory of dynamical systems. II

AUTHOR(S)
Ovchinnikov, Igor V.
PUB. DATE
March 2013
SOURCE
Chaos;Mar2013, Vol. 23 Issue 1, p013108
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This paper is a continuation of the study [Chaos.22.033134] of the relation between the stochastic dynamical systems (DS) and the Witten-type topological field theories (TFT). Here, it is discussed that the stochastic expectation values of a DS must be complemented on the TFT side by (-1)F⁁, where F⁁ is the ghost number operator. The role of this inclusion is to unfold the natural path-integral representation of the TFT, i.e., the Witten index that equals up to a topological constant to the partition function of the stochastic noise, into the physical partition function of TFT/DS. It is also shown that on the DS side, the TFT's wavefunctions are the conditional probability densities.
ACCESSION #
86446949

 

Related Articles

  • Topological field theory of dynamical systems. Ovchinnikov, Igor V. // Chaos;Sep2012, Vol. 22 Issue 3, p033134 

    Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must...

  • Topological Field Theories and Harrison Homology. Cooper, Benjamin // Letters in Mathematical Physics;Apr2013, Vol. 103 Issue 4, p351 

    Tools and arguments developed by Kevin Costello are adapted to families of 'Outer Spaces' or spaces of graphs. This allows us to prove a version of Deligne's conjecture: the Harrison homology associated with a homotopy commutative algebra is naturally a module over a cobordism category of...

  • A THEORY ON EXTENDING ALGORITHMS FOR PARAMETRIC PROBLEMS. Eaves, B. Curtis; Rothblum, Uriel G. // Mathematics of Operations Research;Aug89, Vol. 14 Issue 3, p502 

    Given certain algorithms for certain problems, these algorithms can be incorporated in a lift, solve, and lower sequence to form algorithms for solving parametric versions of the problems. In the first phase of the sequence the parametric problem is lifted to an extended ordered field where it...

  • Stochastic Dominance and Conditional Expectation--An Insurance Theoretical Approach. Borglin, Anders; Keiding, Hans // GENEVA Papers on Risk & Insurance - Theory;Jun2002, Vol. 27 Issue 1, p31 

    We show that the relation of second order stochastic dominance, which has found widespread use in models of economic behavior under uncertainty, may be described in terms of conditional expectation. If a distribution G second order stochastically dominates another distribution F, then there are...

  • Markov processes on Riesz spaces. Vardy, Jessica; Watson, Bruce // Positivity;Jun2012, Vol. 16 Issue 2, p373 

    Measure-free discrete time stochastic processes in Riesz spaces were formulated and studied by Kuo, Labuschagne and Watson. Aspects relating martingales, stopping times, convergence of these processes as well as various decomposition were considered. Here we formulate and study Markov processes...

  • An Upper Bound for Conditional Second Moment of the Solution of a SDE. Yurachkivsky, Andriy // Applied Mathematics;Jan2013, Vol. 4 Issue 1, p135 

    Let 픽 = f(t), t ∈ ℝ+ be a filtration on some probability space and let K denote the class of all 픽-adapted ℝd-valued stochastic processes M such that E(∣M (·)∣2 ∣F(0)) < ∞, E(M(t)∣F(s)) = M(s) for all t > s ≥ 0 and the process...

  • LEVY'S THEOREM AND STRONG CONVERGENCE OF MARTINGALES IN A DUAL SPACE. Saadoune, M. // Acta Mathematica Universitatis Comenianae;2012, Vol. 81 Issue 1, p31 

    We prove Levy's Theorem for a new class of functions taking values from a dual space and we obtain almost sure strong convergence of martingales and mils satisfying various tightness conditions.

  • Conditional expectations associated with quantum states. Niestegge, Gerd // Journal of Mathematical Physics;Apr2005, Vol. 46 Issue 4, p043507 

    An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations always exist; in the quantum case, however, they exist...

  • Covariance tapering for prediction of large spatial data sets in transformed random fields. Hirano, Toshihiro; Yajima, Yoshihiro // Annals of the Institute of Statistical Mathematics;Oct2013, Vol. 65 Issue 5, p913 

    The best linear unbiased predictor (BLUP) is called a kriging predictor and has been widely used to interpolate a spatially correlated random process in scientific areas such as geostatistics. However, if an underlying random field is not Gaussian, the optimality of the BLUP in the mean squared...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics