Publication

Non-explosion principles for branched rough differential equations with unbounded coefficients

2026

Abstract

Expanding upon the work of [LY25], we provide a non-explosion criterion for branched rough differential equations (bRDEs) where we continue to allow for the drift and the rough coefficient to be unbounded in the branched setting. Moreover, by providing a characterization of "pure area" branched rough paths-branched rough paths over the zero path, we provide two different constructions of bRDEs which explode in finite time, and thus demonstrating the sharpness of the criterion. Finally, by realizing a trade-off between the growth of the coefficient of the bRDE and the decay of its higher-order derivatives, we provide a new non-explosion principle for bRDEs which allows for the coefficient to grow even faster than what is provided in [LY25].

Official source

https://infoscience.epfl.ch/entities/publication/0d138959-166a-4bb5-94ca-ea1c10e47acb

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0d138959-166a-4bb5-94ca-ea1c10e47acb

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Related concepts (23)

Principle of explosion

In classical logic, intuitionistic logic and similar logical systems, the principle of explosion (ex falso [sequitur] quodlibet, 'from falsehood, anything [follows]'; or ex contradictione [sequitur] quodlibet), or the principle of Pseudo-Scotus (falsely attributed to Duns Scotus), is the law according to which any statement can be proven from a contradiction. That is, from a contradiction, any proposition (including its negation) can be inferred from it; this is known as deductive explosion.

Law of noncontradiction

In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive. Formally, this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case" holds.

Derivative

In mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

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Non-explosion principles for branched rough differential equations with unbounded coefficients

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