scholarly journals On Copula-Itô processes

2019 ◽  
Vol 7 (1) ◽  
pp. 322-347
Author(s):  
Piotr Jaworski
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Infinitesimal Generator ◽  
Continuous Semigroup ◽  
Tangent Vector ◽  
Parabolic Partial Differential Equation ◽  
Strongly Continuous Semigroup ◽  
Tangent Vector Field ◽  
The Family ◽  
Semigroup Of Transformations

AbstractWe study the dynamics of the family of copulas {Ct}t≥0 of a pair of stochastic processes given by stochastic differential equations (SDE). We associate to it a parabolic partial differential equation (PDE). Having embedded the set of bivariate copulas in a dual of a Sobolev Hilbert space H1 (ℝ2)* we calculate the derivative with respect to t and the *weak topology i.e. the tangent vector field to the image of the curve t → Ct. Furthermore we show that the family {Ct}t≥0 is an orbit of a strongly continuous semigroup of transformations and provide the infinitesimal generator of this semigroup.

scholarly journals Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

2005 ◽  
Vol 2005 (6) ◽  
pp. 607-617 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Parabolic Partial Differential Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

scholarly journals On radial stationary solutions to a model of non-equilibrium growth

2013 ◽  
Vol 24 (3) ◽  
pp. 437-453 ◽  
Author(s):  
CARLOS ESCUDERO ◽  
ROBERT HAKL ◽  
IRENEO PERAL ◽  
PEDRO J. TORRES
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stationary Solutions ◽  
Parabolic Partial Differential Equation ◽  
Radial Solutions ◽  
Variational Techniques ◽  
Existence And Multiplicity ◽  
Equilibrium Growth ◽  
Non Equilibrium

We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

scholarly journals USING GENERALIZED STOCHASTIC METHOD TO EVALUATE PROBABILITY OF CONFLICT IN CONTROLLED AIR TRAFFIC

Aviation ◽  
2007 ◽  
Vol 11 (2) ◽  
pp. 31-36 ◽  
Author(s):  
Vitaly Babak ◽  
Volodymyr Kharchenko ◽  
Volodymyr Vasylyev
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Traffic Safety ◽  
Evaluation Method ◽  
Air Traffic ◽  
Collision Probability ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Potential Conflict ◽  
Infinitesimal Operator

The introduction of the new concepts of air traffic management (ATM) and transition from centralized to decentralized air traffic control (ATC) with the change of traditional ATM to Cooperative ATM sets new tasks and opens new capabilities for air traffic safety systems. This paper is devoted to the problem of evaluating the probability of aircraft collision under the condition of Cooperative ATM, when the necessary information is available to the subjects involved in the decision‐making process. The generalized stochastic conflict probability evaluation method is developed. This method is based on the generalized conflict probability equation for evaluation of potential conflict probability and aircraft collision probability that is derived by taking into account stochastic nature and time correlation of deviation from planned flight trajectory in controlled air traffic. This equation is described as a multi‐dimensional parabolic partial differential equation using a differential (infinitesimal) operator of the multi‐dimensional stochastic process of relative aircraft movement. The common procedure for the prediction of conflict probability is given, and the practical application of the generalized method presented is shown. All equational coefficients of a differential operator for a practical solution of a parabolic partial differential equation are derived. For some conditions, the numerical solution of the conflict probability equation is obtained and illustrated graphically.

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