scholarly journals ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING

2009 ◽  
Vol 09 (03) ◽  
pp. 437-477 ◽  
Author(s):  
AURÉLIEN DEYA ◽  
SAMY TINDEL
Keyword(s):  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Volterra Equations ◽  
Existence And Uniqueness Theorem ◽  
Hölder Exponent ◽  
Local Existence And Uniqueness ◽  
Hurst Coefficient ◽  
Rough Path ◽  
Driving Signal

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent γ > 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent 1/3 < γ < 1/2, we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H > 1/3.

scholarly journals An abstract inverse problem

1991 ◽  
Vol 4 (2) ◽  
pp. 117-128 ◽  
Author(s):  
M. Choulli
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Local Existence ◽  
Sufficient Conditions ◽  
Existence And Uniqueness Theorem ◽  
Local Existence And Uniqueness ◽  
Abstract Integrodifferential Equation

In this paper we consider an inverse problem that corresponds to an abstract integrodifferential equation. First, we prove a local existence and uniqueness theorem. We also show that every continuous solution can be locally extended in a unique way. Finally, we give sufficient conditions for the existence and a stability of the global solution.

The Einstein equation for signature type changing spacetimes

1994 ◽  
Vol 446 (1926) ◽  
pp. 115-126 ◽  
Keyword(s):  
Scalar Field ◽  
Uniqueness Theorem ◽  
Einstein Equation ◽  
Existence And Uniqueness ◽  
Energy Momentum Tensor ◽  
Local Existence ◽  
Momentum Tensor ◽  
Existence And Uniqueness Theorem ◽  
Local Existence And Uniqueness ◽  
Type Change

We give a local existence and uniqueness theorem for solutions of Einstein’s equations with dust energy momentum tensor in the class of m -dimensional, analytic, transverse, signature type changing spacetimes where the initial condi­tions are given on the hypersurface of signature type change. We also prove a similar theorem in the case that the energy momentum tensor represents a scalar field.

scholarly journals Solving Arbitrage Problem on the Financial Market Under the Mixed Fractional Brownian Motion With Hurst Parameter H ∈]1/2,3/4[

2019 ◽  
Vol 11 (1) ◽  
pp. 76
Author(s):  
Eric Djeutcha ◽  
Didier Alain Njamen Njomen ◽  
Louis-Aimé Fono
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Financial Market ◽  
Existence And Uniqueness ◽  
Hurst Parameter ◽  
Existence And Uniqueness Theorem ◽  
Martingale Approximation ◽  
Arbitrage Opportunities ◽  
Mixed Fractional Brownian Motion ◽  
Geometric Fractional Brownian Motion

This study deals with the arbitrage problem on the financial market when the underlying asset follows a mixed fractional Brownian motion. We prove the existence and uniqueness theorem for the mixed geometric fractional Brownian motion equation. The semi-martingale approximation approach to mixed fractional Brownian motion is used to eliminate the arbitrage opportunities.

scholarly journals Local and Global Existence of Solution for Love Type Waves with Past History

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1998
Author(s):  
Mohamed Biomy ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Existence And Uniqueness ◽  
Past History ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linearization Method ◽  
Weak Compactness ◽  
Existence Of Solution ◽  
Local Existence And Uniqueness ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

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