M. Lifshits

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math.PR2026

Ornstein-Uhlenbeck process conditioned to have restricted $L_{2}$ -norm

Frank Aurzada, Mikhail Lifshits, Max Wiegand

We condition an Ornstein-Uhlenbeck process on having an atypically small $L_{2}$ -norm on long time intervals. The weak limit of these conditioned processes is again an Ornstein-Uhlen…

math.PR2026

Estimates of $mm$ -entropy of a stable LÃ©vy process

Viktor Khamzin, Mikhail Lifshits

In the article the $mm$ -entropy (an entropy of a metric measure space) introduced by C. Shannon is evaluated for an $I^\pm$ -stable LÃ©vy process. For $I^\pm < 1$ the double-sided estimates…

math.PR2025

Asymptotic distribution of the derivative of the taut string accompanying Wiener process

Mikhail Lifshits, Andrei Podchishchailov

In the article, we find the asymptotic distribution of the derivative of the taut string accompanying a Wiener process in a strip of fixed width on long time intervals. This enable…

math.PR2024

Brownian motion conditioned to have restricted $L_{2}$ -norm

Frank Aurzada, Mikhail Lifshits, Dominic T. Schickentanz

We condition a Brownian motion on having an atypically small $L_{2}$ -norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.

Ornstein-Uhlenbeck process conditioned to have restricted L2​-norm

Estimates of mm-entropy of a stable LÃ©vy process

Asymptotic distribution of the derivative of the taut string accompanying Wiener process

Brownian motion conditioned to have restricted L2​-norm

Ornstein-Uhlenbeck process conditioned to have restricted $L_{2}$ -norm

Estimates of $mm$ -entropy of a stable LÃ©vy process

Brownian motion conditioned to have restricted $L_{2}$ -norm