7月21日（木）に談話会を開催します．
学外からご参加いただける場合は原則，zoom（オンライン）上での参加をお願いいたします．ご参加の場合は平良（ktaira@fc.ritsumei.ac.jp ）までご連絡ください．
日程：7月21日（木）16:30-19:00
場所：立命館大学BKCキャンパスウエストウイング談話会室（対面とzoomのハイブリッド開催）
16:30-17:30：鈴木良一（立命館大学）
タイトル: Malliavin-Sokorohod calculus for canonical Lévy processes with applications
アブストラクト: In this talk, we deal Malliavin-Sokorohod (MS, in short) calculus for canonical Lévy processes with applications, especially mathematical finance. MS calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of ‘’derivatives” of random variables, such as functionals for Lévy processes, stochastic integrals and stochastic differential equations. MS calculus is also called the stochastic calculus of variations.
The first half of the presentation, we introduce MS calculus for canonical Lévy processes. Especially, we use chaos expansion, derivative operator and increment quotient difference operator for Lévy functionals. Calculations tools about MS calculus are also introduced. By using the results, we next derive a new modified $\Phi$-Sobolev type inequalities for canonical Lévy processes and we also derive concentration inequalities. Moreover, asymptotic estimates for their inequality will be given.
The second half of the presentation will address issues to mathematical finance. In particular, we consider locally risk minimizing hedging strategies, a typical hedging technique in incomplete markets. The presentation will introduce a method using Malliavin analysis, which provides a concrete expression formula and can be applied to numerical analysis and other practical problems. The use of Malliavin analysis provides concrete expression formulas, which can be applied to numerical analysis and other practical applications.
In the remaining time, we will discuss future prospects.
18:00-19:00：磯崎洋（立命館大学）
タイトル：グラフ上のラプラシアンに対する Gel’fand の問題
日本語