# Kei Kobayashi

Assistant Professor of Mathematics

Phone: 212-636-6331

Email: kkobayashi5@fordham.edu

Office: LL 815F

PhD in mathematics, Tufts University, 2011

MS in mathematics, Kanazawa University, 2005

BS in mathematics, Kanazawa University, 2003

- Post-Doc Teaching Associate, The University of Tennessee, 2013-2016
- Lecturer, Tufts University, 2012-2013

My research concerns probability, stochastic processes, and their applications. I am particularly interested in analysis of non-Markovian stochastic processes, including fractional Brownian motion and Levy processes that are composed with random time changes, as well as stochastic differential equations driven by those processes. Such non-Markovian processes provide models for complicated phenomena with memories and have found many important applications in areas such as economics, physics, chemistry, biology, and finance. In terms of the stochastic differential equations, my previous results concern both theory (stochastic integration, the corresponding stochastic calculus, etc.) and its applications (numerical approximation schemes for the solution processes, their associated Fokker-Planck or Kolmogorov equations which may be of fractional order, etc.).

(with S. Jin) Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators. To appear in *BIT Numer. Math.*

(with P. Kerger) Parameter estimation for one-sided heavy-tailed distributions. *Stat. Probab. Lett.* 164 (2020), 108808.

(with J. Lind, A. Starnes) Effect of random time changes on Loewner hulls. *Rev. Mat. Iberoam.* 36, 3 (2020), 771-790.

(with S. Jin) Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients. *J. Math. Anal. Appl.* 476, 2 (2019), 619-636.

(with S. Umarov, M. Hahn) *Beyond the Triangle: Brownian Motion, Ito Calculus, and Fokker-Planck Equation -- Fractional Generalizations.* World Scientific (2018).

(with E. Jum) A strong and weak approximation scheme for stochastic differential equations driven by a time-changed Brownian motion. *Probab. Math. Statist.* 36, 2 (2016), 201-220.

Small ball probabilities for a class of time-changed self-similar processes. *Stat. Probab. Lett.* 110 (2016), 155-161.

(with M. Hahn, S. Umarov) SDEs driven by a time-changed L evy process and their associated time-fractional order pseudo-differential equations. *J. Theor. Probab.* 25, 1 (2012), 262-279.

Stochastic calculus for a time-changed semimartingale and the associated stochastic differential equations. *J. Theor. Probab.* 24, 3 (2011), 789-820.

(with M. Hahn, J. Ryvkina, S. Umarov) On time-changed Gaussian processes and their associated Fokker-Planck-Kolmogorov equations. *Elect. Comm. in Probab.* 16 (2011), 150-164.

(with M. Hahn, S. Umarov) Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion. *Proc. Amer. Math. Soc.* 139 (2011), 691-705.