Results 11 to 20 of about 331 (134)
The geometry of the space of branched rough paths
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 220-251, August 2020., 2020 Abstract We construct an explicit transitive free action of a Banach space of Hölder functions on the space of branched rough paths, which yields in particular a bijection between these two spaces. This endows the space of branched rough paths with the structure of a principal homogeneous space over a Banach space and allows to characterize its ...
Nikolas Tapia, Lorenzo Zambotti
wiley +1 more source
Quasi‐shuffle algebras and renormalisation of rough differential equations
Bulletin of the London Mathematical Society, Volume 52, Issue 1, Page 43-63, February 2020., 2020 Abstract The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on rooted trees known from backward error analysis of B‐series. For this purpose, we present a so‐called arborification of the Hoffman–Ihara theory of quasi‐shuffle ...
Yvain Bruned +2 more
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Uniqueness of stable processes with drift [PDF]
, 2013 Suppose that d ≥ 1 and α ∈ (1, 2). Let Y be a rotationally symmetric α-stable process on R d and b a R-valued measurable function on R belonging to a certain Kato class of Y .
Zhen-Qing Chen, Longmin Wang
semanticscholar +1 more source
Existence and Comparisons for BSDEs in general spaces [PDF]
, 2010 We present a theory of Backward Stochastic Differential Equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the continuity of the filtration, or of the predictable quadratic variations of ...
Samuel N. Cohen, R. Elliott
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On the stability of solutions to conformable stochastic differential equations
, 2020 In this paper, we study the stability of solutions to conformable stochastic differential equations. Firstly, we show the trivial solution are stochastially stable, stochastically asymptotically stable and almost surely exponentially stable, respectively.
Guanli Xiao, Jinrong Wang
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The influence of the noise on the exact solutions of a Kuramoto-Sivashinsky equation
Open Mathematics, 2022 In this article, we take into account the stochastic Kuramoto-Sivashinsky equation forced by multiplicative noise in the Itô sense. To obtain the exact stochastic solutions of the stochastic Kuramoto-Sivashinsky equation, we apply the G′G\frac{{G ...
Albosaily Sahar +4 more
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Open Mathematics, 2022 The Picard iteration method is used to study the existence and uniqueness of solutions for the stochastic Volterra-Levin equation with variable delays. Several sufficient conditions are specified to ensure that the equation has a unique solution.
Jin Shoubo
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Demonstratio Mathematica, 2023 In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed.
Mohammed Wael W. +2 more
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Construction of analytical solutions to systems of two stochastic differential equations
Open Mathematics, 2023 A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a ...
Navickas Zenonas +4 more
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On copulas of self-similar Ito processes
Dependence Modeling, 2021 We characterize the cumulative distribution functions and copulas of two-dimensional self-similar Ito processes, with randomly correlated Wiener margins, as solutions of certain elliptic partial differential equations.
Jaworski Piotr, Krzywda Marcin
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