SDE Symbolic Solver

Stochastic Differential Equation Solver

Enter your stochastic differential equation and get a symbolic solution with steps.

Based on research by Chu-Ching Huang (2011)

Equation Type

Itô SDE

Stratonovich SDE

Process Type

Simulation Settings

Time Start

Time End

Time Steps

Trajectories

Drift Coefficient μ(t, X)

The dt term in dX = μ(t,X)dt + σ(t,X)dW

Diffusion Coefficient σ(t, X)

The dW term in dX = μ(t,X)dt + σ(t,X)dW

Initial Condition X₀

Time Variable

Parameter Values (JSON)

SDE Examples

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Documentation

Using the SDE Solver

1. Equation Input

Enter your stochastic differential equation using standard mathematical notation:

Drift coefficient: The deterministic part (dt term)
Diffusion coefficient: The stochastic part (dW term)
Supported functions: sin, cos, exp, log, sqrt
Parameters must be entered as valid JSON in the parameters field

2. Equation Types

Itô SDE

Standard formulation using Itô calculus. Follows the Itô isometry and has zero expected value for stochastic integrals.

Stratonovich SDE

Uses midpoint evaluation. Follows the classical chain rule and is more natural for physical applications.

3. Supported Processes

Geometric Brownian Motion: dX = μX dt + σX dW
Ornstein-Uhlenbeck: dX = θ(μ − X) dt + σ dW
Vasicek / CIR: Interest rate models
Jump Diffusion: Continuous diffusion + Poisson jumps

4. Simulation Parameters

Time range: Define the simulation interval [t₀, T]
Time steps: Number of discretization points (Euler–Maruyama)
Trajectories: Number of independent sample paths

About

This web application provides symbolic solutions and numerical simulations for Stochastic Differential Equations (SDEs). It implements methods based on the research of Chu-Ching Huang (2011), extended with modern web technologies.

Reference: Huang, C. C. (2011). Python Solver for Stochastic Differential Equations. Matimyas Matematika, 34(1-2), 87–97.

Features

Symbolic solution of Itô and Stratonovich SDEs
Step-by-step solution derivation with MathJax rendering
Euler–Maruyama numerical simulation
Interactive Plotly trajectory charts
Export to PDF and LaTeX

Technical Stack

Backend: Python · FastAPI · SymPy
Frontend: HTML · Tailwind CSS · Vanilla JS
Visualization: Plotly.js
Math Typesetting: MathJax 3
License: MIT

Developer

Ramanambonona Ambinintsoa, PhD

Modelling & Computational Economics — ENS Antananarivo

Stochastic Differential Equation Solver

Equation Type

Process Type

Simulation Settings

Final Solution

Simulation Results

SDE Examples

Documentation

Using the SDE Solver

1. Equation Input

2. Equation Types

Itô SDE

Stratonovich SDE

3. Supported Processes

4. Simulation Parameters

About