# Questions tagged [stochastic-calculus]

Questions about stochastic calculus in Mathematica, for example how to use ItoProcess and RandomFunction.

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### Gillespie (stochastic simulation) algorithm

I want to apply the Gillespie algorithm to a set of reactions. First, I run the source code presented here, and then run my model: ...
• 167
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### Log scale of y-axis is still very small [closed]

I am trying to use LogPlot of Mathematica to rewrite only y-axis (not x-axis) of the plot as log scale. But the y-axis is still very small. By the following code <...
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1 vote
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### Product of two Ito processes

I am in the process of learning to use Mathematica for doing stochastic calculus. I can do Ito's lemma by symbolic manipulation, substitutions, expansions and simplifications. However, I feel like ...
47 views

### Identifying the parameter that flips the solution

I have solved a system of ODEs numerically. As the plot shows, the solution SolJx is positive for the parameters I have chosen. However, if you decrease (more ...
• 479
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### Evaluating an integral of geometric Brownian motion

I am a Mathematica novice. For an operations research application, I am trying to work with the following wealth process in Mathematica, $$d W_t = (\rho W_t + P_t) dt\ ,$$ where $P_t$ is a stream ...
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### How do I simulate an ItoProcess that is not supposed to become negative?

I have a process that is similar to a Cox Ingersoll Ross process. Like a CIR process this process does not become negative. However, when I define the process with ItoProcess and I simulate it with ...
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1 vote
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### How can I use RandomFunction to solve an SDE in reverse time?

I am working with a problem of the Ito-stochastic differential form given by $$\mathrm{d}x=g(x,t)\,\mathrm{d}t+f(x,t)\,\mathrm{d}W,$$ where $W$ is a Wiener process. I furthermore have to satisfy the ...
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### Mean of an Ito Process

I would like to compute the mean of s[t] which is given by the first equation in these coupled stochastic ordinary differential equation ...
1 vote
264 views

### Coupled stochastic differential equation [closed]

I am trying to solve the following coupled system of stochastic differential equations: $\qquad \dot{x}(t)=y(t)\,\eta(t)$ $\qquad \dot{y}(t)=x(t)\,\eta(t)$ $x$ and $y$ are functions to be solved for ...
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### Can built-in functions deal with stochastic delay differential equations (SDDE)?

I know that functions like NDSolve can deal with delay differential equations and in the meanwhile, functions like ItoProcess ...
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### How can I can plot a stochastic process? [closed]

How I can plot the following stochastic process using mathmatica
1 vote
89 views

### Mean of ItoProcess

I've defined the following ItoProcess ...
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