Small ball probabilities for integrals of weighted Brownian motion

Dunker, Thomas; Li, W.V.; Linde, Werner

doi:10.1016/s0167-7152(99)00098-x

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2024

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“…The following theorem and lemma are about the probability estimation of Brownian motion balls, which are the basis for the theorem in this article. The proof of the theorem can be found in [6].…”

Section: Technical Lemmas and Theoremsmentioning

confidence: 99%

Onsager-Machlup functional for stochastic differential equations with additive noise

Zhang,

2024

Preprint

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This paper is devoted to studying the Onsager-Machlup functional for stochastic differential equations (SDEs) with additive noise of the α-Hölder, 0 < α < 1/4, dXt = f (t, Xt)dt + g(t)dWt. When the diffusion term of SDEs is not a fixed constant, we obtain the Onsager-Machlup functional. This function is the Lagrangian giving the most probable transition path connecting metastable states for stochastic processes driven by additive noise. This is done by introducing new measurable norms and applying an appropriate version of the Girsanov transformation. Moreover, we provide examples of numerical simulations, including a one-dimensional SDE and a fast-slow SDE for multiscale stochastic volatility models. MSC2020 subject classifications: Primary 82C35, 60H10; secondary 37H10

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Section: Technical Lemmas and Theoremsmentioning

confidence: 99%

Onsager-Machlup functional for stochastic differential equations with additive noise

Zhang,

2024

Preprint

View full text Add to dashboard Cite

show abstract

Small ball probabilities for integrals of weighted Brownian motion

Cited by 1 publication

References 9 publications

Onsager-Machlup functional for stochastic differential equations with additive noise

Onsager-Machlup functional for stochastic differential equations with additive noise

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