On a skew stable Lévy process (Lecture 3)

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• Andrey Pilipenko (National Academy of Sciences of Ukraine)
• Friday 02 August 2024, 10:00-11:00
• Seminar Room 2, Newton Institute.

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SSD - Stochastic systems for anomalous diffusion

The skew Brownian motion is a strong Markov process which behaves like a Brownian motion until hitting zero and exhibits an asymmetry at zero. We address the following question: what is a natural counterpart of the skew Brownian motion in the situation that an underlying Brownian motion is replaced with a stable Lévy process with finite mean and infinite variance. We define a skew stable Lévy process X as a limit of a sequence of stable Lévy processes which are perturbed at zero. We derive a formula for the resolvent of X and show that X is a solution to a stochastic differential equation with a local time.

This talk is part of the Isaac Newton Institute Seminar Series series.

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