PyProcess is a Python class library used to exactly simulate stochastic processes, and their properties.

See realized examples of processes here: pyprocess.70percentfatfree.com

In this library, you can simulate the following random processes:

Continuous Diffusions
- Brownian Motion
- Geometric Brownian Motion
- CEV
- CIR
- Square Bessel Process 
- Ornstein Uhlenbeck process
- Time-integrated Ornstein Uhlenbeck process
- Levy Processes
- Bessel Process (coming soon)
- Fractional Brownian Motion (coming soon)

Jump Diffusions
- Gamma process
- Variance-gamma process
- Geometric Gamma process
- Inverse Gaussian process *NEW*
- Normal Inverse Gaussian process *NEW*

Step Processes
- Renewal process
- Poisson process
- Compound poisson process
- marked-poisson process
- Fractional poisson process (coming soon)



To create a stochastic project instance, you need to give the class the specific parameters and any time or space constraints.
For example, if we wish to create a non-standard Brownian motion instance (named Wiener_motion) which has parameters 
'mu' and 'sigma', we use:


parameters = {'mu':-1, 'sigma':2}
time_space_constraints = {'startTime': 0, 'startPosition':2}
process = Wiener_process( parameters, time_space_constraints )

process.get_mean_at(10)
# -8.0

process.generate_position_at(10)
# -1.96953969194

times = range(10)
process.generate_sample_path(times)
# [(0, 2.0), (1, 3.5504434920777763), (2, 2.8862861385211374), (3, 2.835569957404396), (4, 3.114651632088956), (5, 2.983357771156665), (6, 2.55760572607476), (7, 2.2188866076280434), (8, 6.528248392922263), (9, 8.349381153333603)]


Most importantly about this library is the ability to condition process on endpoints to. For example, suppose we want to 
tie the browian motion above at a endpoint (10,0) (ie. at time 10, the process is at 0. This is simple, continuing from 
above we add the constraints to time_space_constraints:

time_space_constraints['endTime':10]
time_space_contraints['endPosition':10]
process = Wiener_process( parameters, time_space_constraints )

process.get_mean_at(9)
# 0.2

process.generate_position_at(9)
# -1.33602629698


times = range(10)
process.generate_sample_path(times)
#[(0, 2.0), (1, 2.031211212004885), (2, 0.5046601471443315), (3, -0.39302356242482717), (4, -1.4515387073784005), (5, 0.023279992315228704), (6, 0.5196539154794165), (7, -1.7891276719165035), (8, -4.564491110511355), (9, -3.2776199543473057), (10, 0.0)]


There are more examples and tricks in the examples.py file.