Pankaj Saha
PhD Scholar @ IIT Guwahati
Department of Mathematics

Pankaj Saha

PhD Scholar in Mathematics

Primary research interests in Stochastic Differential Equations (SDEs), Large Deviation Principle (LDP), and Probability Theory. M.Sc. Graduate from Indian Institute of Technology (IIT) Indore with exposure to mathematical finance, reaction-diffusion systems, and weak convergence methods.

$$\mathrm{d}X_t = b(X_t)\mathrm{d}t + \sigma(X_t)\mathrm{d}W_t, \quad \lim_{\epsilon \to 0} \epsilon \log \mathbb{E}\left[e^{-\frac{1}{\epsilon} h(X^\epsilon)}\right] = -\inf_{x \in \mathcal{S}} \{h(x) + I(x)\}$$
Stochastic Differential System & Laplace Principle formulation
Research Focus Contact Information
4 National Exams Qualified
5+ Academic Workshops
Core Domains

Research Interests

Focusing on modern probabilistic frameworks, stochastic dynamics, and large deviation asymptotics for complex mathematical models.

Stochastic Differential Equations (SDEs)

Modeling dynamic systems subject to random noise, analyzing existence, uniqueness of strong solutions, and asymptotic behavior.

$$\mathrm{d}X_t = b(t, X_t)\mathrm{d}t + \sigma(t, X_t)\mathrm{d}W_t$$

Large Deviation Principle (LDP)

Investigating asymptotic properties of rare events using weak convergence techniques established by Budhiraja and Dupuis.

$$\mathbb{P}(X_\epsilon \in A) \approx \exp\left(-\frac{1}{\epsilon} \inf_{x \in A} I(x)\right)$$

Mathematical Finance

Risk management, option pricing dynamics, financial econometrics, and stochastic volatility modeling in financial markets.

$$\mathrm{d}S_t = \mu S_t \mathrm{d}t + \sigma S_t \mathrm{d}W_t$$

Stochastic Processes

Analysis of Markov chains, Brownian motion, martingale theory, and application to biological predator-prey systems.

$$\mathbb{E}[M_t \mid \mathcal{F}_s] = M_s \quad (s \le t)$$

Probability Theory & Reaction-Diffusion

Measure-theoretic probability, infinite dimensional spaces, Polish spaces, and reaction-diffusion PDEs under stochastic perturbation.

$$\frac{\partial u}{\partial t} = D \nabla^2 u + f(u) + \sigma(u)\dot{W}$$
Academic Journey

Education Background

Current Affiliation
2026 – Present

Doctor of Philosophy (PhD) in Mathematics

Indian Institute of Technology (IIT) Guwahati, India

Pursuing doctoral research in stochastic analysis, probability, and mathematical modeling.

Master's Degree
Aug 2023 – Jul 2025

Master of Science (M.Sc.) in Mathematics

Indian Institute of Technology (IIT) Indore, India

Thesis Supervisor: Dr. Debopriya Mukherjee

Bachelor's Degree
Jul 2019 – Jun 2022

Bachelor of Science (B.Sc.)

Sukanta Mahavidyalaya, North Bengal University, India

Honours in Mathematics with Generic Elective in Computer Science.

Senior Secondary (10+2)
2019

Higher Secondary Examination

Maynaguri High School, WBCHSE, West Bengal

Secondary (10th)
2017

Secondary Examination

Maynaguri High School, WBBSE, West Bengal

Competitive Excellence

National Examinations Qualified

2026

GATE (MA)

Graduate Aptitude Test in Engineering - Mathematics

Qualified National Level Exam
2023

IIT-JAM

Joint Admission Test for M.Sc. (Mathematics)

Qualified for IIT Admission
2022

CUET PG

Common University Entrance Test Postgraduate

Qualified National Entrance
2019

WBJEE

West Bengal Joint Entrance Examination

Qualified State Entrance
Continuous Learning

Academic Activities & Workshops

15–16 Feb 2025

Mathematical Finance and Risk Management

Instructor: Dr. Neelesh S. Upadhye • NPTEL

Workshop covering modern portfolio theory, risk metrics, option pricing, and stochastic volatility modeling.

9–10 Jan 2025

Financial Econometrics and Panel Data Analysis Workshop

Jaya Prakash Narayan National Centre of Excellence in HSS, IIT Indore

Hands-on training in panel data modeling, stationary time-series analysis, and econometric methods.

22 Oct 2024

Differential Equation Solvers & Applications

Department of Mathematics, IIT Indore

Seminar on numerical ODE/PDE solvers, stability analysis, and computational mathematical tools.

13 May 2024

AIS - Stochastic Processes and Applications

Hosted by IIT Guwahati

Advanced Instructional School on Markov chains, random walks, and SDE theory hosted at IIT Guwahati.

22 Jan 2024

IEEE CIS Workshop on Women in Artificial Intelligence

Organized by IEEE MP Section – CIS Chapter at IIT Indore

Focusing on machine learning paradigms, AI methodologies, and intelligent computational systems.

Curriculum & Competencies

Coursework & Skills Explorer

Pure Mathematics

Real Analysis Functional Analysis Complex Analysis Measure Theory Probability Theory Linear Algebra Topology

Applied Mathematics

Probability & Statistical Methods Ordinary Differential Equations (ODE) Partial Differential Equations (PDE) Numerical Analysis Machine Learning

Technical & Programming Skills

R & MATLAB Intermediate
C Programming Intermediate
LaTeX & Technical Writing Intermediate
Python & C++ Basic Proficiency

Linguistic Proficiency

English (Professional) Bengali (Native / Fluent) Hindi (Fluent)
Get in Touch

Contact & Communication

Feel free to reach out for research discussions, academic collaborations, or questions.

IIT Guwahati Email

pankajsaha@iitg.ac.in

Personal Email

ponkojs318@gmail.com

IIT Indore Alum Email

msc2303141010@alum.iiti.ac.in

LinkedIn Profile

linkedin.com/in/pankaj-saha-7ab770209

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