👩🏼🏫 Outreach in mathematics
Apr 20, 2026·
·
1 min read
Emmanuel G.
Stochastic Volterra Integral Equations: Asymptotic StationarityStochastic Volterra Integral Equations: Asymptotic Stationarity!
Citation
Here are some publications associated to the topic:
(2026).
On Path-dependent Volterra Integral Equations: Strong Well-posedness and Stochastic Numerics..
Submitted for publication.
(2025).
On a Stationarity Theory for Stochastic Volterra Integral Equations.
Submitted for publication.
Video
Youtube:
{{< youtube RTC2KIboZws >}}
Math block:
$$\begin{align*} &\sum_{z \in \mathbb{C} \setminus \{-1\}: z^\alpha=-1} \text{Res}(J_{\alpha}(t, \cdot), z) = \frac{1}{2\pi i} \oint_{\Gamma_{\gamma, \delta, R}} J_{\alpha}(t, z) \, dz = \frac{1}{2\pi i}\int_{\textit{Br}(\gamma, R)} J_{\alpha}(t, z) \, dz + \frac{1}{2\pi i}\int_{C^+} J_{\alpha}(t, z) \, dz \\ &\quad \hspace{1.5cm} + \frac{1}{2\pi i}\int_{C_R^+} J_{\alpha}(t, z) \, dz - \frac{1}{2\pi i}\int_{\textit{H}(\delta, \frac{1}{R})} J_{\alpha}(t, z) \, dz + \frac{1}{2\pi i}\int_{C_R^-} J_{\alpha}(t, z) \, dz + \frac{1}{2\pi i}\int_{C^-} J_{\alpha}(t, z) \, dz.\end{align*} $$Latex code
\begin{align*}
&\sum_{z \in \mathbb{C} \setminus \{-1\}: z^\alpha=-1} \text{Res}(J_{\alpha}(t, \cdot), z)
= \frac{1}{2\pi i} \oint_{\Gamma_{\gamma, \delta, R}} J_{\alpha}(t, z) \, dz
= \frac{1}{2\pi i}\int_{\textit{Br}(\gamma, R)} J_{\alpha}(t, z) \, dz + \frac{1}{2\pi i}\int_{C^+} J_{\alpha}(t, z) \, dz \\
&\quad \hspace{1.5cm} + \frac{1}{2\pi i}\int_{C_R^+} J_{\alpha}(t, z) \, dz - \frac{1}{2\pi i}\int_{\textit{H}(\delta, \frac{1}{R})} J_{\alpha}(t, z) \, dz + \frac{1}{2\pi i}\int_{C_R^-} J_{\alpha}(t, z) \, dz + \frac{1}{2\pi i}\int_{C^-} J_{\alpha}(t, z) \, dz.
\end{align*}
Stochastic Volterra Processes
Stochastic Differential Equations
Fourier-Laplace Transforms
Jordan-Cauchy Residue Theorem
Regular Variation
Tauberian Theorems
Limit Theorems
Confluence
Authors
Emmanuel G.
(he/him)
Researcher in Mathematics and Applications
I am a Research Scientist in Mathematics at LPSM Sorbonne Université, working on stochastic analysis, optimal control, diffusion models, and statistics, with applications to mathematical finance and machine learning.